फलन \(\sin x\) का काल क्या है?
What is the period of the function \(\sin x\)?
#trigonometric-functions
#period
#sine
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A \(\pi\)
B \(\frac{\pi}{2}\)
C \(2\pi\)
D \(4\pi\)
Explanation opens after your attempt
Correct Answer
C. \(2\pi\)
Step 1
Concept
\(\sin x\) repeats its value after every \(2\pi\). In exams first identify the basic function.
Step 2
Why this answer is correct
The correct answer is C. \(2\pi\). \(\sin x\) repeats its value after every \(2\pi\). In exams first identify the basic function.
Step 3
Exam Tip
\(\sin x\) हर \(2\pi\) के बाद अपना मान दोहराता है। परीक्षा में काल पूछने पर सबसे पहले मूल फलन पहचानें।
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फलन \(\cos x\) का परिसर क्या है?
What is the range of the function \(\cos x\)?
#trigonometric-functions
#range
#cosine
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A ([0,1])
B ([-1,1])
C (\(-\infty,\infty\))
D \([1,\infty\))
Explanation opens after your attempt
Correct Answer
B. ([-1,1])
Step 1
Concept
The value of \(\cos x\) always lies between (-1) and (1). The end values are included in the range.
Step 2
Why this answer is correct
The correct answer is B. ([-1,1]). The value of \(\cos x\) always lies between (-1) and (1). The end values are included in the range.
Step 3
Exam Tip
\(\cos x\) का मान हमेशा (-1) और (1) के बीच रहता है। परिसर में अंतिम मान भी शामिल होते हैं।
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निम्न में से कौन-सा फलन विषम है?
Which of the following functions is odd?
#trigonometric-functions
#odd-function
#sine
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A \(\cos x\)
B \(\sec x\)
C \(\sin x\)
D \(\cos^2 x\)
Explanation opens after your attempt
Correct Answer
C. \(\sin x\)
Step 1
Concept
Since (\sin(-x)=-\sin x), \(\sin x\) is an odd function. For an odd function, (f(-x)=-f(x)).
Step 2
Why this answer is correct
The correct answer is C. \(\sin x\). Since (\sin(-x)=-\sin x), \(\sin x\) is an odd function. For an odd function, (f(-x)=-f(x)).
Step 3
Exam Tip
क्योंकि (\sin(-x)=-\sin x), इसलिए \(\sin x\) विषम फलन है। विषम फलन में (f(-x)=-f(x)) होता है।
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निम्न में से कौन-सा फलन सम है?
Which of the following functions is even?
#trigonometric-functions
#even-function
#cosine
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A \(\sin x\)
B \(\tan x\)
C \(\cot x\)
D \(\cos x\)
Explanation opens after your attempt
Correct Answer
D. \(\cos x\)
Step 1
Concept
Since (\cos(-x)=\cos x), \(\cos x\) is an even function. For an even function, (f(-x)=f(x)).
Step 2
Why this answer is correct
The correct answer is D. \(\cos x\). Since (\cos(-x)=\cos x), \(\cos x\) is an even function. For an even function, (f(-x)=f(x)).
Step 3
Exam Tip
क्योंकि (\cos(-x)=\cos x), इसलिए \(\cos x\) सम फलन है। सम फलन में (f(-x)=f(x)) होता है।
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पहचान \(\sin^2 x+\cos^2 x\) का मान क्या है?
What is the value of the identity \(\sin^2 x+\cos^2 x\)?
#trigonometric-identities
#basic-property
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A (0)
B (1)
C \(\tan x\)
D \(\sec x\)
Explanation opens after your attempt
Step 1
Concept
The basic identity is \(\sin^2 x+\cos^2 x=1\). Remembering it helps in many questions.
Step 2
Why this answer is correct
The correct answer is B. (1). The basic identity is \(\sin^2 x+\cos^2 x=1\). Remembering it helps in many questions.
Step 3
Exam Tip
मूल पहचान \(\sin^2 x+\cos^2 x=1\) होती है। इसे याद रखना कई प्रश्नों में काम आता है।
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फलन \(\tan x\) का काल क्या है?
What is the period of the function \(\tan x\)?
#trigonometric-functions
#period
#tangent
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A \(\pi\)
B \(2\pi\)
C \(\frac{\pi}{2}\)
D \(4\pi\)
Explanation opens after your attempt
Correct Answer
A. \(\pi\)
Step 1
Concept
\(\tan x\) repeats its value after every \(\pi\). The period of \(\tan x\) and \(\cot x\) is \(\pi\).
Step 2
Why this answer is correct
The correct answer is A. \(\pi\). \(\tan x\) repeats its value after every \(\pi\). The period of \(\tan x\) and \(\cot x\) is \(\pi\).
Step 3
Exam Tip
\(\tan x\) हर \(\pi\) के बाद अपना मान दोहराता है। \(\tan x\) और \(\cot x\) का काल \(\pi\) होता है।
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फलन \(\sec x\) किसका व्युत्क्रम है?
The function \(\sec x\) is the reciprocal of which function?
#reciprocal-identities
#secant
#cosine
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A \(\sin x\)
B \(\tan x\)
C \(\cos x\)
D \(\cot x\)
Explanation opens after your attempt
Correct Answer
C. \(\cos x\)
Step 1
Concept
\(\sec x=\frac{1}{\cos x}\). Learn reciprocal relations in pairs.
Step 2
Why this answer is correct
The correct answer is C. \(\cos x\). \(\sec x=\frac{1}{\cos x}\). Learn reciprocal relations in pairs.
Step 3
Exam Tip
\(\sec x=\frac{1}{\cos x}\) होता है। व्युत्क्रम संबंधों को जोड़ी बनाकर याद करें।
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फलन \(\cosec x\) किसका व्युत्क्रम है?
The function \(\cosec x\) is the reciprocal of which function?
#reciprocal-identities
#cosecant
#sine
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A \(\cos x\)
B \(\sin x\)
C \(\tan x\)
D \(\sec x\)
Explanation opens after your attempt
Correct Answer
B. \(\sin x\)
Step 1
Concept
\(\cosec x=\frac{1}{\sin x}\). Remember that \(\cosec x\) is related to \(\sin x\).
Step 2
Why this answer is correct
The correct answer is B. \(\sin x\). \(\cosec x=\frac{1}{\sin x}\). Remember that \(\cosec x\) is related to \(\sin x\).
Step 3
Exam Tip
\(\cosec x=\frac{1}{\sin x}\) होता है। ध्यान रखें कि \(\cosec x\) का संबंध \(\sin x\) से है।
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\(\tan x\) को \(\sin x\) और \(\cos x\) के रूप में कैसे लिखा जाता है?
How is \(\tan x\) written in terms of \(\sin x\) and \(\cos x\)?
#quotient-identities
#tangent
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A \(\frac{\cos x}{\sin x}\)
B \(\sin x\cos x\)
C \(\frac{\sin x}{\cos x}\)
D \(\frac{1}{\sin x}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{\sin x}{\cos x}\)
Step 1
Concept
\(\tan x=\frac{\sin x}{\cos x}\) is a basic quotient identity. In such questions, check numerator and denominator carefully.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{\sin x}{\cos x}\). \(\tan x=\frac{\sin x}{\cos x}\) is a basic quotient identity. In such questions, check numerator and denominator carefully.
Step 3
Exam Tip
\(\tan x=\frac{\sin x}{\cos x}\) मूल अनुपात पहचान है। ऐसे प्रश्नों में अंश और हर को ध्यान से देखें।
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\(\cot x\) को \(\sin x\) और \(\cos x\) के रूप में कैसे लिखा जाता है?
How is \(\cot x\) written in terms of \(\sin x\) and \(\cos x\)?
#quotient-identities
#cotangent
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A \(\frac{\sin x}{\cos x}\)
B \(\frac{\cos x}{\sin x}\)
C \(\sin x+\cos x\)
D \(\frac{1}{\cos x}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{\cos x}{\sin x}\)
Step 1
Concept
\(\cot x=\frac{\cos x}{\sin x}\). \(\tan x\) and \(\cot x\) are reciprocals of each other.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{\cos x}{\sin x}\). \(\cot x=\frac{\cos x}{\sin x}\). \(\tan x\) and \(\cot x\) are reciprocals of each other.
Step 3
Exam Tip
\(\cot x=\frac{\cos x}{\sin x}\) होता है। \(\tan x\) और \(\cot x\) एक-दूसरे के व्युत्क्रम हैं।
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फलन \(\sin x\) का परिसर क्या है?
What is the range of the function \(\sin x\)?
#trigonometric-functions
#range
#sine
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A ([-1,1])
B \([0,\infty\))
C (\(-\infty,\infty\))
D ([0,1])
Explanation opens after your attempt
Correct Answer
A. ([-1,1])
Step 1
Concept
The value of \(\sin x\) lies from (-1) to (1). Remembering the graph helps find the range quickly.
Step 2
Why this answer is correct
The correct answer is A. ([-1,1]). The value of \(\sin x\) lies from (-1) to (1). Remembering the graph helps find the range quickly.
Step 3
Exam Tip
\(\sin x\) का मान (-1) से (1) तक होता है। ग्राफ याद रखने से परिसर जल्दी मिलता है।
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फलन \(\tan x\) का परिसर क्या है?
What is the range of the function \(\tan x\)?
#trigonometric-functions
#range
#tangent
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A ([-1,1])
B ([0,1])
C (\(-\infty,\infty\))
D \([1,\infty\))
Explanation opens after your attempt
Correct Answer
C. (\(-\infty,\infty\))
Step 1
Concept
\(\tan x\) can take all real values. Therefore, its range is (\(-\infty,\infty\)).
Step 2
Why this answer is correct
The correct answer is C. (\(-\infty,\infty\)). \(\tan x\) can take all real values. Therefore, its range is (\(-\infty,\infty\)).
Step 3
Exam Tip
\(\tan x\) सभी वास्तविक मान ले सकता है। इसलिए इसका परिसर (\(-\infty,\infty\)) है।
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\(\sec^2 x-\tan^2 x\) का मान क्या है?
What is the value of \(\sec^2 x-\tan^2 x\)?
#trigonometric-identities
#secant
#tangent
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A (0)
B \(\sin x\)
C (2)
D (1)
Explanation opens after your attempt
Step 1
Concept
Since \(\sec^2 x=1+\tan^2 x\), \(\sec^2 x-\tan^2 x=1\). Use the identity in the correct direction.
Step 2
Why this answer is correct
The correct answer is D. (1). Since \(\sec^2 x=1+\tan^2 x\), \(\sec^2 x-\tan^2 x=1\). Use the identity in the correct direction.
Step 3
Exam Tip
क्योंकि \(\sec^2 x=1+\tan^2 x\), इसलिए \(\sec^2 x-\tan^2 x=1\)। पहचान को सही दिशा में प्रयोग करें।
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\(\cosec^2 x-\cot^2 x\) का मान क्या है?
What is the value of \(\cosec^2 x-\cot^2 x\)?
#trigonometric-identities
#cosecant
#cotangent
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A \(\cos x\)
B (1)
C (0)
D \(\tan x\)
Explanation opens after your attempt
Step 1
Concept
Since \(\cosec^2 x=1+\cot^2 x\), the difference is (1). This identity is linked to \(\sin^2 x+\cos^2 x=1\).
Step 2
Why this answer is correct
The correct answer is B. (1). Since \(\cosec^2 x=1+\cot^2 x\), the difference is (1). This identity is linked to \(\sin^2 x+\cos^2 x=1\).
Step 3
Exam Tip
क्योंकि \(\cosec^2 x=1+\cot^2 x\), अंतर (1) होगा। यह पहचान \(\sin^2 x+\cos^2 x=1\) से जुड़ी है।
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यदि \(\sin x=0\), तो (x=0) पर \(\cos x\) का मान क्या है?
If \(\sin x=0\), what is the value of \(\cos x\) at (x=0)?
#standard-values
#cosine
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A (-1)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
At (x=0), \(\cos 0=1\). Remembering standard angle values helps in easy questions.
Step 2
Why this answer is correct
The correct answer is C. (1). At (x=0), \(\cos 0=1\). Remembering standard angle values helps in easy questions.
Step 3
Exam Tip
(x=0) पर \(\cos 0=1\) होता है। मानक कोणों के मान याद रखना आसान प्रश्नों में मदद करता है।
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\(\sin 0\) का मान क्या है?
What is the value of \(\sin 0\)?
#standard-values
#sine
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A (1)
B (0)
C (-1)
D \(\frac{1}{2}\)
Explanation opens after your attempt
Step 1
Concept
\(\sin 0=0\) is a standard value. In exams, remember the values for (0), \(\frac{\pi}{2}\), and \(\pi\).
Step 2
Why this answer is correct
The correct answer is B. (0). \(\sin 0=0\) is a standard value. In exams, remember the values for (0), \(\frac{\pi}{2}\), and \(\pi\).
Step 3
Exam Tip
\(\sin 0=0\) एक मानक मान है। परीक्षा में (0), \(\frac{\pi}{2}\) और \(\pi\) के मान जरूर याद रखें।
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\(\tan 0\) का मान क्या है?
What is the value of \(\tan 0\)?
#standard-values
#tangent
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A \(\frac{1}{2}\)
B (1)
C (0)
D अपरिभाषित / Undefined
Explanation opens after your attempt
Step 1
Concept
\(\tan 0=\frac{\sin 0}{\cos 0}=\frac{0}{1}=0\). The quotient identity gives the value easily.
Step 2
Why this answer is correct
The correct answer is C. (0). \(\tan 0=\frac{\sin 0}{\cos 0}=\frac{0}{1}=0\). The quotient identity gives the value easily.
Step 3
Exam Tip
\(\tan 0=\frac{\sin 0}{\cos 0}=\frac{0}{1}=0\)। अनुपात पहचान से मान आसानी से निकलेगा।
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\(\sin \frac{\pi}{2}\) का मान क्या है?
What is the value of \(\sin \frac{\pi}{2}\)?
#standard-values
#sine
#unit-circle
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A (0)
B (1)
C (-1)
D \(\frac{1}{2}\)
Explanation opens after your attempt
Step 1
Concept
At \(\frac{\pi}{2}\), the value of \(\sin x\) is (1). The unit circle helps remember this value quickly.
Step 2
Why this answer is correct
The correct answer is B. (1). At \(\frac{\pi}{2}\), the value of \(\sin x\) is (1). The unit circle helps remember this value quickly.
Step 3
Exam Tip
\(\frac{\pi}{2}\) पर \(\sin x\) का मान (1) होता है। यूनिट सर्कल से यह मान जल्दी याद होता है।
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\(\cos \frac{\pi}{2}\) का मान क्या है?
What is the value of \(\cos \frac{\pi}{2}\)?
#standard-values
#cosine
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A (1)
B अपरिभाषित / Undefined
C (0)
D (-1)
Explanation opens after your attempt
Step 1
Concept
At \(\frac{\pi}{2}\), the value of \(\cos x\) is (0). A standard angle table reduces mistakes.
Step 2
Why this answer is correct
The correct answer is C. (0). At \(\frac{\pi}{2}\), the value of \(\cos x\) is (0). A standard angle table reduces mistakes.
Step 3
Exam Tip
\(\frac{\pi}{2}\) पर \(\cos x\) का मान (0) है। मानक कोणों की तालिका से गलती कम होती है।
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(\sin\(\pi-x\)) किसके बराबर है?
What is (\sin\(\pi-x\)) equal to?
#trigonometric-properties
#allied-angles
#sine
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A \(-\sin x\)
B \(\cos x\)
C \(\sin x\)
D \(-\cos x\)
Explanation opens after your attempt
Correct Answer
C. \(\sin x\)
Step 1
Concept
\(\pi-x\) lies in the second quadrant and \(\sin x\) remains positive there. Hence (\sin\(\pi-x\)=\sin x).
Step 2
Why this answer is correct
The correct answer is C. \(\sin x\). \(\pi-x\) lies in the second quadrant and \(\sin x\) remains positive there. Hence (\sin\(\pi-x\)=\sin x).
Step 3
Exam Tip
\(\pi-x\) दूसरे चतुर्थांश में होता है और वहाँ \(\sin x\) धनात्मक रहता है। इसलिए (\sin\(\pi-x\)=\sin x)।
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(\cos\(\pi-x\)) किसके बराबर है?
What is (\cos\(\pi-x\)) equal to?
#trigonometric-properties
#allied-angles
#cosine
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A \(\cos x\)
B \(-\cos x\)
C \(\sin x\)
D \(-\sin x\)
Explanation opens after your attempt
Correct Answer
B. \(-\cos x\)
Step 1
Concept
In the second quadrant, \(\cos x\) is negative. Therefore, (\cos\(\pi-x\)=-\cos x).
Step 2
Why this answer is correct
The correct answer is B. \(-\cos x\). In the second quadrant, \(\cos x\) is negative. Therefore, (\cos\(\pi-x\)=-\cos x).
Step 3
Exam Tip
दूसरे चतुर्थांश में \(\cos x\) ऋणात्मक होता है। इसलिए (\cos\(\pi-x\)=-\cos x)।
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(\tan\(\pi+x\)) किसके बराबर है?
What is (\tan\(\pi+x\)) equal to?
#periodicity
#tangent
#allied-angles
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A \(-\tan x\)
B \(\cot x\)
C \(\tan x\)
D \(-\cot x\)
Explanation opens after your attempt
Correct Answer
C. \(\tan x\)
Step 1
Concept
The period of \(\tan x\) is \(\pi\), so (\tan\(\pi+x\)=\tan x). Using period gives the answer quickly.
Step 2
Why this answer is correct
The correct answer is C. \(\tan x\). The period of \(\tan x\) is \(\pi\), so (\tan\(\pi+x\)=\tan x). Using period gives the answer quickly.
Step 3
Exam Tip
\(\tan x\) का काल \(\pi\) है, इसलिए (\tan\(\pi+x\)=\tan x)। काल का उपयोग करके उत्तर जल्दी मिलता है।
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(\sin(-x)) किसके बराबर है?
What is (\sin(-x)) equal to?
#odd-function
#sine
#negative-angle
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A \(\sin x\)
B \(-\sin x\)
C \(\cos x\)
D \(-\cos x\)
Explanation opens after your attempt
Correct Answer
B. \(-\sin x\)
Step 1
Concept
\(\sin x\) is an odd function, so (\sin(-x)=-\sin x). Identify even-odd properties quickly.
Step 2
Why this answer is correct
The correct answer is B. \(-\sin x\). \(\sin x\) is an odd function, so (\sin(-x)=-\sin x). Identify even-odd properties quickly.
Step 3
Exam Tip
\(\sin x\) विषम फलन है, इसलिए (\sin(-x)=-\sin x)। सम-विषम गुण जल्दी पहचानें।
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(\cos(-x)) किसके बराबर है?
What is (\cos(-x)) equal to?
#even-function
#cosine
#negative-angle
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A \(-\cos x\)
B \(\sin x\)
C \(\cos x\)
D \(-\sin x\)
Explanation opens after your attempt
Correct Answer
C. \(\cos x\)
Step 1
Concept
\(\cos x\) is an even function, so (\cos(-x)=\cos x). Use even-odd properties for negative angle questions.
Step 2
Why this answer is correct
The correct answer is C. \(\cos x\). \(\cos x\) is an even function, so (\cos(-x)=\cos x). Use even-odd properties for negative angle questions.
Step 3
Exam Tip
\(\cos x\) सम फलन है, इसलिए (\cos(-x)=\cos x)। ऋण कोण वाले प्रश्नों में सम-विषम गुण लगाएँ।
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(\tan(-x)) किसके बराबर है?
What is (\tan(-x)) equal to?
#odd-function
#tangent
#negative-angle
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A \(\tan x\)
B \(-\tan x\)
C \(\cot x\)
D \(-\cot x\)
Explanation opens after your attempt
Correct Answer
B. \(-\tan x\)
Step 1
Concept
\(\tan x\) is an odd function, so (\tan(-x)=-\tan x). This can also be understood from \(\frac{\sin x}{\cos x}\).
Step 2
Why this answer is correct
The correct answer is B. \(-\tan x\). \(\tan x\) is an odd function, so (\tan(-x)=-\tan x). This can also be understood from \(\frac{\sin x}{\cos x}\).
Step 3
Exam Tip
\(\tan x\) विषम फलन है, इसलिए (\tan(-x)=-\tan x)। इसे \(\frac{\sin x}{\cos x}\) से भी समझ सकते हैं।
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पहले चतुर्थांश में \(\sin x\) का चिन्ह क्या होता है?
What is the sign of \(\sin x\) in the first quadrant?
#quadrants
#signs
#sine
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A ऋणात्मक / Negative
B शून्य / Zero
C धनात्मक / Positive
D अपरिभाषित / Undefined
Explanation opens after your attempt
Correct Answer
C. धनात्मक / Positive
Step 1
Concept
In the first quadrant, all trigonometric functions are positive. Remember the quadrant sign table.
Step 2
Why this answer is correct
The correct answer is C. धनात्मक / Positive. In the first quadrant, all trigonometric functions are positive. Remember the quadrant sign table.
Step 3
Exam Tip
पहले चतुर्थांश में सभी त्रिकोणमितीय फलन धनात्मक होते हैं। चतुर्थांश संकेत तालिका याद रखें।
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दूसरे चतुर्थांश में \(\cos x\) का चिन्ह क्या होता है?
What is the sign of \(\cos x\) in the second quadrant?
#quadrants
#signs
#cosine
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A धनात्मक / Positive
B ऋणात्मक / Negative
C शून्य / Zero
D अपरिभाषित / Undefined
Explanation opens after your attempt
Correct Answer
B. ऋणात्मक / Negative
Step 1
Concept
In the second quadrant, only \(\sin x\) and \(\cosec x\) are positive. Therefore, \(\cos x\) is negative.
Step 2
Why this answer is correct
The correct answer is B. ऋणात्मक / Negative. In the second quadrant, only \(\sin x\) and \(\cosec x\) are positive. Therefore, \(\cos x\) is negative.
Step 3
Exam Tip
दूसरे चतुर्थांश में केवल \(\sin x\) और \(\cosec x\) धनात्मक होते हैं। इसलिए \(\cos x\) ऋणात्मक होता है।
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तीसरे चतुर्थांश में \(\tan x\) का चिन्ह क्या होता है?
What is the sign of \(\tan x\) in the third quadrant?
#quadrants
#signs
#tangent
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A ऋणात्मक / Negative
B शून्य / Zero
C धनात्मक / Positive
D अपरिभाषित / Undefined
Explanation opens after your attempt
Correct Answer
C. धनात्मक / Positive
Step 1
Concept
In the third quadrant, \(\tan x\) and \(\cot x\) are positive. The sign rule gives the answer directly.
Step 2
Why this answer is correct
The correct answer is C. धनात्मक / Positive. In the third quadrant, \(\tan x\) and \(\cot x\) are positive. The sign rule gives the answer directly.
Step 3
Exam Tip
तीसरे चतुर्थांश में \(\tan x\) और \(\cot x\) धनात्मक होते हैं। संकेत नियम से उत्तर सीधे मिलता है।
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चौथे चतुर्थांश में \(\sin x\) का चिन्ह क्या होता है?
What is the sign of \(\sin x\) in the fourth quadrant?
#quadrants
#signs
#sine
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A धनात्मक / Positive
B ऋणात्मक / Negative
C शून्य / Zero
D अपरिभाषित / Undefined
Explanation opens after your attempt
Correct Answer
B. ऋणात्मक / Negative
Step 1
Concept
In the fourth quadrant, \(\cos x\) and \(\sec x\) are positive. Hence \(\sin x\) is negative.
Step 2
Why this answer is correct
The correct answer is B. ऋणात्मक / Negative. In the fourth quadrant, \(\cos x\) and \(\sec x\) are positive. Hence \(\sin x\) is negative.
Step 3
Exam Tip
चौथे चतुर्थांश में \(\cos x\) और \(\sec x\) धनात्मक होते हैं। इसलिए \(\sin x\) ऋणात्मक होता है।
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(\sin\(2\pi+x\)) किसके बराबर है?
What is (\sin\(2\pi+x\)) equal to?
#periodicity
#sine
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A \(\sin x\)
B \(-\sin x\)
C \(\cos x\)
D \(-\cos x\)
Explanation opens after your attempt
Correct Answer
A. \(\sin x\)
Step 1
Concept
The period of \(\sin x\) is \(2\pi\), so (\sin\(2\pi+x\)=\sin x). Remember periodic identities.
Step 2
Why this answer is correct
The correct answer is A. \(\sin x\). The period of \(\sin x\) is \(2\pi\), so (\sin\(2\pi+x\)=\sin x). Remember periodic identities.
Step 3
Exam Tip
\(\sin x\) का काल \(2\pi\) है, इसलिए (\sin\(2\pi+x\)=\sin x)। काल वाली पहचान याद रखें।
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(\cos\(2\pi+x\)) किसके बराबर है?
What is (\cos\(2\pi+x\)) equal to?
#periodicity
#cosine
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A \(-\cos x\)
B \(\sin x\)
C \(\cos x\)
D \(-\sin x\)
Explanation opens after your attempt
Correct Answer
C. \(\cos x\)
Step 1
Concept
\(\cos x\) repeats after every \(2\pi\). Therefore, (\cos\(2\pi+x\)=\cos x).
Step 2
Why this answer is correct
The correct answer is C. \(\cos x\). \(\cos x\) repeats after every \(2\pi\). Therefore, (\cos\(2\pi+x\)=\cos x).
Step 3
Exam Tip
\(\cos x\) हर \(2\pi\) पर दोहरता है। इसलिए (\cos\(2\pi+x\)=\cos x)।
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(\sin\(\frac{\pi}{2}-x\)) किसके बराबर है?
What is (\sin\(\frac{\pi}{2}-x\)) equal to?
#cofunction-identities
#sine
#cosine
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A \(\sin x\)
B \(-\sin x\)
C \(\cos x\)
D \(-\cos x\)
Explanation opens after your attempt
Correct Answer
C. \(\cos x\)
Step 1
Concept
By the complementary angle identity, (\sin\(\frac{\pi}{2}-x\)=\cos x). With \(\frac{\pi}{2}\), the function changes.
Step 2
Why this answer is correct
The correct answer is C. \(\cos x\). By the complementary angle identity, (\sin\(\frac{\pi}{2}-x\)=\cos x). With \(\frac{\pi}{2}\), the function changes.
Step 3
Exam Tip
पूरक कोण पहचान से (\sin\(\frac{\pi}{2}-x\)=\cos x) होता है। \(\frac{\pi}{2}\) के साथ फलन बदलता है।
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(\cos\(\frac{\pi}{2}-x\)) किसके बराबर है?
What is (\cos\(\frac{\pi}{2}-x\)) equal to?
#cofunction-identities
#cosine
#sine
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A \(\cos x\)
B \(-\cos x\)
C \(-\sin x\)
D \(\sin x\)
Explanation opens after your attempt
Correct Answer
D. \(\sin x\)
Step 1
Concept
By the complementary angle identity, (\cos\(\frac{\pi}{2}-x\)=\sin x). In such questions, \(\sin x\) and \(\cos x\) interchange.
Step 2
Why this answer is correct
The correct answer is D. \(\sin x\). By the complementary angle identity, (\cos\(\frac{\pi}{2}-x\)=\sin x). In such questions, \(\sin x\) and \(\cos x\) interchange.
Step 3
Exam Tip
पूरक कोण पहचान से (\cos\(\frac{\pi}{2}-x\)=\sin x) होता है। ऐसे प्रश्नों में \(\sin x\) और \(\cos x\) आपस में बदलते हैं।
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(\tan\(\frac{\pi}{2}-x\)) किसके बराबर है?
What is (\tan\(\frac{\pi}{2}-x\)) equal to?
#cofunction-identities
#tangent
#cotangent
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A \(\tan x\)
B \(\cot x\)
C \(-\tan x\)
D \(-\cot x\)
Explanation opens after your attempt
Correct Answer
B. \(\cot x\)
Step 1
Concept
For a complementary angle with \(\frac{\pi}{2}\), \(\tan x\) changes to \(\cot x\). Remember cofunction identities.
Step 2
Why this answer is correct
The correct answer is B. \(\cot x\). For a complementary angle with \(\frac{\pi}{2}\), \(\tan x\) changes to \(\cot x\). Remember cofunction identities.
Step 3
Exam Tip
\(\frac{\pi}{2}\) के पूरक कोण में \(\tan x\) बदलकर \(\cot x\) हो जाता है। पूरक पहचान याद रखें।
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फलन \(\sec x\) का काल क्या है?
What is the period of the function \(\sec x\)?
#period
#secant
#reciprocal
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A \(\pi\)
B \(\frac{\pi}{2}\)
C \(2\pi\)
D \(4\pi\)
Explanation opens after your attempt
Correct Answer
C. \(2\pi\)
Step 1
Concept
The period of \(\sec x\) is \(2\pi\), like \(\cos x\). The reciprocal function keeps the related basic period.
Step 2
Why this answer is correct
The correct answer is C. \(2\pi\). The period of \(\sec x\) is \(2\pi\), like \(\cos x\). The reciprocal function keeps the related basic period.
Step 3
Exam Tip
\(\sec x\) का काल \(\cos x\) जैसा \(2\pi\) होता है। व्युत्क्रम फलन का काल मूल फलन से जुड़ा रहता है।
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फलन \(\cot x\) का काल क्या है?
What is the period of the function \(\cot x\)?
#period
#cotangent
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A \(\pi\)
B \(2\pi\)
C \(\frac{\pi}{2}\)
D \(3\pi\)
Explanation opens after your attempt
Correct Answer
A. \(\pi\)
Step 1
Concept
\(\cot x\) repeats its value after every \(\pi\). Both \(\tan x\) and \(\cot x\) have period \(\pi\).
Step 2
Why this answer is correct
The correct answer is A. \(\pi\). \(\cot x\) repeats its value after every \(\pi\). Both \(\tan x\) and \(\cot x\) have period \(\pi\).
Step 3
Exam Tip
\(\cot x\) हर \(\pi\) के बाद अपना मान दोहराता है। \(\tan x\) और \(\cot x\) दोनों का काल \(\pi\) है।
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फलन \(\cosec x\) का काल क्या है?
What is the period of the function \(\cosec x\)?
#period
#cosecant
#reciprocal
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A \(\frac{\pi}{2}\)
B \(\pi\)
C \(2\pi\)
D \(4\pi\)
Explanation opens after your attempt
Correct Answer
C. \(2\pi\)
Step 1
Concept
\(\cosec x\) is the reciprocal of \(\sin x\) and its period is \(2\pi\). Use reciprocal relation to identify the period.
Step 2
Why this answer is correct
The correct answer is C. \(2\pi\). \(\cosec x\) is the reciprocal of \(\sin x\) and its period is \(2\pi\). Use reciprocal relation to identify the period.
Step 3
Exam Tip
\(\cosec x\) \(\sin x\) का व्युत्क्रम है और इसका काल \(2\pi\) है। व्युत्क्रम संबंध से काल पहचानें।
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\(\sec x\) का परिसर क्या है?
What is the range of \(\sec x\)?
#range
#secant
#reciprocal
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A ((-1,1))
B ([-1,1])
C (\(-\infty,\infty\))
D (\(-\infty,-1]\cup[1,\infty\))
Explanation opens after your attempt
Correct Answer
D. (\(-\infty,-1]\cup[1,\infty\))
Step 1
Concept
\(\sec x=\frac{1}{\cos x}\) and \(\cos x\) lies in ([-1,1]). Hence \(\sec x\) is greater than or equal to (1) or less than or equal to (-1).
Step 2
Why this answer is correct
The correct answer is D. (\(-\infty,-1]\cup[1,\infty\)). \(\sec x=\frac{1}{\cos x}\) and \(\cos x\) lies in ([-1,1]). Hence \(\sec x\) is greater than or equal to (1) or less than or equal to (-1).
Step 3
Exam Tip
\(\sec x=\frac{1}{\cos x}\) है और \(\cos x\) का मान ([-1,1]) में होता है। इसलिए \(\sec x\) का मान (1) से बड़ा या (-1) से छोटा होता है।
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\(\cosec x\) का परिसर क्या है?
What is the range of \(\cosec x\)?
#range
#cosecant
#reciprocal
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A (\(-\infty,-1]\cup[1,\infty\))
B ([-1,1])
C ((0,1))
D (\(-\infty,\infty\))
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,-1]\cup[1,\infty\))
Step 1
Concept
\(\cosec x=\frac{1}{\sin x}\). Therefore, its range is (\(-\infty,-1]\cup[1,\infty\)).
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,-1]\cup[1,\infty\)). \(\cosec x=\frac{1}{\sin x}\). Therefore, its range is (\(-\infty,-1]\cup[1,\infty\)).
Step 3
Exam Tip
\(\cosec x=\frac{1}{\sin x}\) है। इसलिए इसका परिसर (\(-\infty,-1]\cup[1,\infty\)) होता है।
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\(\tan x\) कहाँ अपरिभाषित होता है?
Where is \(\tan x\) undefined?
#domain
#tangent
#undefined
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A \(\cos x=0\)
B \(\sin x=0\)
C \(\tan x=0\)
D \(\sec x=1\)
Explanation opens after your attempt
Correct Answer
A. \(\cos x=0\)
Step 1
Concept
\(\tan x=\frac{\sin x}{\cos x}\), so it is undefined when \(\cos x=0\). A fraction is not defined when the denominator is zero.
Step 2
Why this answer is correct
The correct answer is A. \(\cos x=0\). \(\tan x=\frac{\sin x}{\cos x}\), so it is undefined when \(\cos x=0\). A fraction is not defined when the denominator is zero.
Step 3
Exam Tip
\(\tan x=\frac{\sin x}{\cos x}\) है, इसलिए \(\cos x=0\) पर यह अपरिभाषित होता है। हर शून्य होने पर भिन्न परिभाषित नहीं रहती।
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\(\cot x\) कहाँ अपरिभाषित होता है?
Where is \(\cot x\) undefined?
#domain
#cotangent
#undefined
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A \(\cos x=0\)
B \(\sin x=0\)
C \(\tan x=1\)
D \(\sec x=0\)
Explanation opens after your attempt
Correct Answer
B. \(\sin x=0\)
Step 1
Concept
\(\cot x=\frac{\cos x}{\sin x}\), so it is undefined when \(\sin x=0\). Always check the denominator carefully.
Step 2
Why this answer is correct
The correct answer is B. \(\sin x=0\). \(\cot x=\frac{\cos x}{\sin x}\), so it is undefined when \(\sin x=0\). Always check the denominator carefully.
Step 3
Exam Tip
\(\cot x=\frac{\cos x}{\sin x}\) है, इसलिए \(\sin x=0\) पर यह अपरिभाषित होता है। हर को हमेशा ध्यान से देखें।
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\(\sec x\) कहाँ अपरिभाषित होता है?
Where is \(\sec x\) undefined?
#domain
#secant
#undefined
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A \(\sin x=0\)
B \(\tan x=0\)
C \(\cos x=0\)
D \(\cot x=0\)
Explanation opens after your attempt
Correct Answer
C. \(\cos x=0\)
Step 1
Concept
\(\sec x=\frac{1}{\cos x}\), so it is undefined when \(\cos x=0\). In reciprocal functions, the denominator cannot be zero.
Step 2
Why this answer is correct
The correct answer is C. \(\cos x=0\). \(\sec x=\frac{1}{\cos x}\), so it is undefined when \(\cos x=0\). In reciprocal functions, the denominator cannot be zero.
Step 3
Exam Tip
\(\sec x=\frac{1}{\cos x}\) है, इसलिए \(\cos x=0\) पर यह अपरिभाषित होता है। व्युत्क्रम फलनों में हर शून्य नहीं हो सकता।
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\(\cosec x\) कहाँ अपरिभाषित होता है?
Where is \(\cosec x\) undefined?
#domain
#cosecant
#undefined
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A \(\cos x=0\)
B \(\sin x=0\)
C \(\tan x=0\)
D \(\sec x=1\)
Explanation opens after your attempt
Correct Answer
B. \(\sin x=0\)
Step 1
Concept
\(\cosec x=\frac{1}{\sin x}\), so it is undefined when \(\sin x=0\). In a reciprocal, the denominator function must not be zero.
Step 2
Why this answer is correct
The correct answer is B. \(\sin x=0\). \(\cosec x=\frac{1}{\sin x}\), so it is undefined when \(\sin x=0\). In a reciprocal, the denominator function must not be zero.
Step 3
Exam Tip
\(\cosec x=\frac{1}{\sin x}\) है, इसलिए \(\sin x=0\) पर यह अपरिभाषित होता है। व्युत्क्रम में नीचे वाला फलन शून्य नहीं होना चाहिए।
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यदि \(\sin x=\frac{3}{5}\) और (x) प्रथम चतुर्थांश में है, तो \(\cos x\) का मान क्या है?
If \(\sin x=\frac{3}{5}\) and (x) is in the first quadrant, what is the value of \(\cos x\)?
#identity
#first-quadrant
#cosine
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A \(\frac{3}{5}\)
B \(\frac{5}{4}\)
C \(\frac{4}{5}\)
D \(-\frac{4}{5}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{4}{5}\)
Step 1
Concept
Using \(\sin^2 x+\cos^2 x=1\), \(\cos x=\frac{4}{5}\). In the first quadrant, \(\cos x\) is positive.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{4}{5}\). Using \(\sin^2 x+\cos^2 x=1\), \(\cos x=\frac{4}{5}\). In the first quadrant, \(\cos x\) is positive.
Step 3
Exam Tip
\(\sin^2 x+\cos^2 x=1\) से \(\cos x=\frac{4}{5}\) मिलता है। प्रथम चतुर्थांश में \(\cos x\) धनात्मक होता है।
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यदि \(\cos x=\frac{12}{13}\) और (x) प्रथम चतुर्थांश में है, तो \(\sin x\) का मान क्या है?
If \(\cos x=\frac{12}{13}\) and (x) is in the first quadrant, what is the value of \(\sin x\)?
#identity
#first-quadrant
#sine
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A \(\frac{5}{13}\)
B \(\frac{12}{13}\)
C \(\frac{13}{5}\)
D -\(\frac{5}{13}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{5}{13}\)
Step 1
Concept
From \(\sin^2 x=1-\cos^2 x\), \(\sin x=\frac{5}{13}\). In the first quadrant, the positive value is taken.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5}{13}\). From \(\sin^2 x=1-\cos^2 x\), \(\sin x=\frac{5}{13}\). In the first quadrant, the positive value is taken.
Step 3
Exam Tip
\(\sin^2 x=1-\cos^2 x\) से \(\sin x=\frac{5}{13}\) मिलता है। प्रथम चतुर्थांश में मान धनात्मक लिया जाता है।
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यदि \(\tan x=\frac{7}{24}\) और (x) प्रथम चतुर्थांश में है, तो \(\sec x\) का मान क्या है?
If \(\tan x=\frac{7}{24}\) and (x) is in the first quadrant, what is the value of \(\sec x\)?
#identity
#tangent
#secant
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A \(\frac{24}{25}\)
B \(\frac{25}{24}\)
C \(\frac{7}{25}\)
D \(\frac{25}{7}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{25}{24}\)
Step 1
Concept
Using \(\sec^2 x=1+\tan^2 x\), \(\sec x=\frac{25}{24}\). In the first quadrant, \(\sec x\) is positive.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{25}{24}\). Using \(\sec^2 x=1+\tan^2 x\), \(\sec x=\frac{25}{24}\). In the first quadrant, \(\sec x\) is positive.
Step 3
Exam Tip
\(\sec^2 x=1+\tan^2 x\) लगाने पर \(\sec x=\frac{25}{24}\) मिलता है। प्रथम चतुर्थांश में \(\sec x\) धनात्मक होता है।
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यदि \(\cot x=\frac{8}{15}\) और (x) प्रथम चतुर्थांश में है, तो \(\cosec x\) का मान क्या है?
If \(\cot x=\frac{8}{15}\) and (x) is in the first quadrant, what is the value of \(\cosec x\)?
#identity
#cotangent
#cosecant
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A \(\frac{15}{17}\)
B \(\frac{17}{15}\)
C \(\frac{8}{17}\)
D \(\frac{17}{8}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{17}{15}\)
Step 1
Concept
From \(\cosec^2 x=1+\cot^2 x\), \(\cosec x=\frac{17}{15}\). Take the positive value in the first quadrant.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{17}{15}\). From \(\cosec^2 x=1+\cot^2 x\), \(\cosec x=\frac{17}{15}\). Take the positive value in the first quadrant.
Step 3
Exam Tip
\(\cosec^2 x=1+\cot^2 x\) से \(\cosec x=\frac{17}{15}\) मिलता है। प्रथम चतुर्थांश में धनात्मक मान लें।
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(\sin\(\pi+x\)) किसके बराबर है?
What is (\sin\(\pi+x\)) equal to?
#allied-angles
#sine
#quadrants
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A \(\sin x\)
B \(\cos x\)
C \(-\sin x\)
D \(-\cos x\)
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Correct Answer
C. \(-\sin x\)
Step 1
Concept
\(\pi+x\) lies in the third quadrant and \(\sin x\) is negative there. Hence (\sin\(\pi+x\)=-\sin x).
Step 2
Why this answer is correct
The correct answer is C. \(-\sin x\). \(\pi+x\) lies in the third quadrant and \(\sin x\) is negative there. Hence (\sin\(\pi+x\)=-\sin x).
Step 3
Exam Tip
\(\pi+x\) तीसरे चतुर्थांश में आता है और वहाँ \(\sin x\) ऋणात्मक होता है। इसलिए (\sin\(\pi+x\)=-\sin x)।
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(\cos\(\pi+x\)) किसके बराबर है?
What is (\cos\(\pi+x\)) equal to?
#allied-angles
#cosine
#quadrants
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A \(\cos x\)
B \(-\cos x\)
C \(\sin x\)
D \(-\sin x\)
Explanation opens after your attempt
Correct Answer
B. \(-\cos x\)
Step 1
Concept
\(\pi+x\) is in the third quadrant and \(\cos x\) is negative there. Therefore, (\cos\(\pi+x\)=-\cos x).
Step 2
Why this answer is correct
The correct answer is B. \(-\cos x\). \(\pi+x\) is in the third quadrant and \(\cos x\) is negative there. Therefore, (\cos\(\pi+x\)=-\cos x).
Step 3
Exam Tip
\(\pi+x\) तीसरे चतुर्थांश में है और वहाँ \(\cos x\) ऋणात्मक होता है। इसलिए (\cos\(\pi+x\)=-\cos x)।
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निम्न में से कौन-सी पहचान सही है?
Which of the following identities is correct?
#trigonometric-identities
#tangent
#secant
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A \(\sec^2 x+\tan^2 x=1\)
B \(\sin^2 x-\cos^2 x=1\)
C \(\tan x=\frac{\cos x}{\sin x}\)
D \(1+\tan^2 x=\sec^2 x\)
Explanation opens after your attempt
Correct Answer
D. \(1+\tan^2 x=\sec^2 x\)
Step 1
Concept
The correct identity is \(1+\tan^2 x=\sec^2 x\). In identity-based questions, check signs and fractions carefully.
Step 2
Why this answer is correct
The correct answer is D. \(1+\tan^2 x=\sec^2 x\). The correct identity is \(1+\tan^2 x=\sec^2 x\). In identity-based questions, check signs and fractions carefully.
Step 3
Exam Tip
सही पहचान \(1+\tan^2 x=\sec^2 x\) है। पहचान आधारित प्रश्नों में चिन्ह और भिन्न को सावधानी से देखें।
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