यदि (\tan \theta+\tan\(\pi-\theta\)=r), तो (r) का मान क्या है?
If (\tan \theta+\tan\(\pi-\theta\)=r), what is the value of (r)?
#trigonometric-functions
#allied-angles
#simplification
A \(\tan \theta\)
B \(2\tan \theta\)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
( \tan\(\pi-\theta\)=-\tan \theta), so the sum is (0). In exams allied angle sign gives the answer quickly.
Step 2
Why this answer is correct
The correct answer is C. (0). ( \tan\(\pi-\theta\)=-\tan \theta), so the sum is (0). In exams allied angle sign gives the answer quickly.
Step 3
Exam Tip
(\tan\(\pi-\theta\)=-\tan \theta), इसलिए योग (0) होता है। परीक्षा में allied angle sign से उत्तर तुरंत मिलता है।
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(\tan\(2\pi-\theta\)) का मान क्या होगा?
What is the value of (\tan\(2\pi-\theta\))?
#trigonometric-functions
#allied-angles
#tangent
A \(\tan \theta\)
B \(-\tan \theta\)
C \(\cot \theta\)
D \(-\cot \theta\)
Explanation opens after your attempt
Correct Answer
B. \(-\tan \theta\)
Step 1
Concept
\(2\pi-\theta\) is in the fourth quadrant where tangent is negative. In exams derive tangent from sine and cosine signs.
Step 2
Why this answer is correct
The correct answer is B. \(-\tan \theta\). \(2\pi-\theta\) is in the fourth quadrant where tangent is negative. In exams derive tangent from sine and cosine signs.
Step 3
Exam Tip
\(2\pi-\theta\) चतुर्थ चतुर्थांश में है जहां tangent ऋणात्मक होता है। परीक्षा में sine और cosine के sign से tangent निकालें।
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(\cos\(\pi+\theta\)) का मान क्या है?
What is the value of (\cos\(\pi+\theta\))?
#trigonometric-functions
#allied-angles
#cosine
A \(\cos \theta\)
B \(\sin \theta\)
C \(-\cos \theta\)
D \(-\sin \theta\)
Explanation opens after your attempt
Correct Answer
C. \(-\cos \theta\)
Step 1
Concept
\( \pi+\theta\) is in the third quadrant and cosine is negative. In exams recall the sign table quickly.
Step 2
Why this answer is correct
The correct answer is C. \(-\cos \theta\). \( \pi+\theta\) is in the third quadrant and cosine is negative. In exams recall the sign table quickly.
Step 3
Exam Tip
\(\pi+\theta\) तृतीय चतुर्थांश में है और cosine ऋणात्मक होता है। परीक्षा में sign table तुरंत याद करें।
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(\sin\(\pi+\theta\)) का मान क्या है?
What is the value of (\sin\(\pi+\theta\))?
#trigonometric-functions
#allied-angles
#sine
A \(\sin \theta\)
B \(-\sin \theta\)
C \(\cos \theta\)
D \(-\cos \theta\)
Explanation opens after your attempt
Correct Answer
B. \(-\sin \theta\)
Step 1
Concept
\( \pi+\theta\) is in the third quadrant where sine is negative. In exams identifying allied angles is important.
Step 2
Why this answer is correct
The correct answer is B. \(-\sin \theta\). \( \pi+\theta\) is in the third quadrant where sine is negative. In exams identifying allied angles is important.
Step 3
Exam Tip
\(\pi+\theta\) तृतीय चतुर्थांश में है जहां sine ऋणात्मक होता है। परीक्षा में allied angle पहचानना जरूरी है।
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(\tan\(\pi-\theta\)) का मान क्या होगा?
What is the value of (\tan\(\pi-\theta\))?
#trigonometric-functions
#allied-angles
#tangent
A \(\tan \theta\)
B \(-\tan \theta\)
C \(\cot \theta\)
D (1)
Explanation opens after your attempt
Correct Answer
B. \(-\tan \theta\)
Step 1
Concept
\( \pi-\theta\) is in the second quadrant and tangent is negative. In exams pay special attention to the sign of tangent.
Step 2
Why this answer is correct
The correct answer is B. \(-\tan \theta\). \( \pi-\theta\) is in the second quadrant and tangent is negative. In exams pay special attention to the sign of tangent.
Step 3
Exam Tip
\(\pi-\theta\) द्वितीय चतुर्थांश में है और tangent ऋणात्मक होता है। परीक्षा में tangent के sign पर विशेष ध्यान दें।
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(\cos\(\pi-\theta\)) का मान क्या है?
What is the value of (\cos\(\pi-\theta\))?
#trigonometric-functions
#allied-angles
#cosine
A \(-\cos \theta\)
B \(\cos \theta\)
C \(\sin \theta\)
D \(-\sin \theta\)
Explanation opens after your attempt
Correct Answer
A. \(-\cos \theta\)
Step 1
Concept
\( \pi-\theta\) is in the second quadrant where cosine is negative. In exams always apply quadrant sign.
Step 2
Why this answer is correct
The correct answer is A. \(-\cos \theta\). \( \pi-\theta\) is in the second quadrant where cosine is negative. In exams always apply quadrant sign.
Step 3
Exam Tip
\(\pi-\theta\) द्वितीय चतुर्थांश में है जहां cosine ऋणात्मक होता है। परीक्षा में चतुर्थांश का चिन्ह जरूर लगाएं।
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(\sin\(\pi-\theta\)) का मान क्या है?
What is the value of (\sin\(\pi-\theta\))?
#trigonometric-functions
#allied-angles
#sine
A \(-\sin \theta\)
B \(\cos \theta\)
C \(\sin \theta\)
D \(-\cos \theta\)
Explanation opens after your attempt
Correct Answer
C. \(\sin \theta\)
Step 1
Concept
\( \pi-\theta\) lies in the second quadrant and sine remains positive. In exams remember allied angle formulas.
Step 2
Why this answer is correct
The correct answer is C. \(\sin \theta\). \( \pi-\theta\) lies in the second quadrant and sine remains positive. In exams remember allied angle formulas.
Step 3
Exam Tip
\(\pi-\theta\) द्वितीय चतुर्थांश में आता है और sine धनात्मक रहता है। परीक्षा में allied angle formula याद रखें।
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(\frac{\cos\(2\pi-x\)}{\sin\(\pi+x\)}) का सरल मान क्या है?
What is the simplified value of (\frac{\cos\(2\pi-x\)}{\sin\(\pi+x\)})?
#allied-angles
#simplification
#cotangent
A \(\tan x\)
B -\(\cot x\)
C \(\cot x\)
D -\(\tan x\)
Explanation opens after your attempt
Correct Answer
B. -\(\cot x\)
Step 1
Concept
(\cos\(2\pi-x\)=\cos x) and (\sin\(\pi+x\)=-\sin x). Hence the value is \(-\cot x\).
Step 2
Why this answer is correct
The correct answer is B. -\(\cot x\). (\cos\(2\pi-x\)=\cos x) and (\sin\(\pi+x\)=-\sin x). Hence the value is \(-\cot x\).
Step 3
Exam Tip
(\cos\(2\pi-x\)=\cos x) और (\sin\(\pi+x\)=-\sin x) है। इसलिए मान \(-\cot x\) है।
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(\frac{\sin\(\pi-x\)}{\cos\(\pi+x\)}) का सरल मान क्या है?
What is the simplified value of (\frac{\sin\(\pi-x\)}{\cos\(\pi+x\)})?
#allied-angles
#simplification
#tangent
A -\(\tan x\)
B \(\tan x\)
C -\(\cot x\)
D \(\cot x\)
Explanation opens after your attempt
Correct Answer
A. -\(\tan x\)
Step 1
Concept
(\sin\(\pi-x\)=\sin x) and (\cos\(\pi+x\)=-\cos x). Therefore, the fraction is \(-\tan x\).
Step 2
Why this answer is correct
The correct answer is A. -\(\tan x\). (\sin\(\pi-x\)=\sin x) and (\cos\(\pi+x\)=-\cos x). Therefore, the fraction is \(-\tan x\).
Step 3
Exam Tip
(\sin\(\pi-x\)=\sin x) और (\cos\(\pi+x\)=-\cos x) होता है। इसलिए भिन्न \(-\tan x\) है।
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(\tan\(\frac{3\pi}{2}+x\)) किसके बराबर है?
What is (\tan\(\frac{3\pi}{2}+x\)) equal to?
#allied-angles
#tangent
#cotangent
A \(\tan x\)
B -\(\tan x\)
C -\(\cot x\)
D \(\cot x\)
Explanation opens after your attempt
Correct Answer
C. -\(\cot x\)
Step 1
Concept
At \(\frac{3\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{3\pi}{2}+x\)=-\cot x).
Step 2
Why this answer is correct
The correct answer is C. -\(\cot x\). At \(\frac{3\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{3\pi}{2}+x\)=-\cot x).
Step 3
Exam Tip
\(\frac{3\pi}{2}+x\) पर \(\tan\) बदलकर \(\cot\) होता है और चिन्ह ऋणात्मक है। इसलिए (\tan\(\frac{3\pi}{2}+x\)=-\cot x)।
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(\cos\(\frac{3\pi}{2}-x\)) किसके बराबर है?
What is (\cos\(\frac{3\pi}{2}-x\)) equal to?
#allied-angles
#cosine
#cofunction
A \(\cos x\)
B \(\sin x\)
C -\(\sin x\)
D -\(\cos x\)
Explanation opens after your attempt
Correct Answer
C. -\(\sin x\)
Step 1
Concept
\(\frac{3\pi}{2}-x\) is related to the third quadrant. \(\cos\) changes to \(\sin\) with a negative sign.
Step 2
Why this answer is correct
The correct answer is C. -\(\sin x\). \(\frac{3\pi}{2}-x\) is related to the third quadrant. \(\cos\) changes to \(\sin\) with a negative sign.
Step 3
Exam Tip
\(\frac{3\pi}{2}-x\) तीसरे चतुर्थांश से जुड़ा है। \(\cos\) बदलकर \(\sin\) होता है और चिन्ह ऋणात्मक रहता है।
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(\sin\(\frac{3\pi}{2}+x\)) किसके बराबर है?
What is (\sin\(\frac{3\pi}{2}+x\)) equal to?
#allied-angles
#sine
#cofunction
A -\(\cos x\)
B \(\cos x\)
C \(\sin x\)
D -\(\sin x\)
Explanation opens after your attempt
Correct Answer
A. -\(\cos x\)
Step 1
Concept
In the form \(\frac{3\pi}{2}+x\), \(\sin\) changes to \(\cos\) with a negative sign. Hence the answer is \(-\cos x\).
Step 2
Why this answer is correct
The correct answer is A. -\(\cos x\). In the form \(\frac{3\pi}{2}+x\), \(\sin\) changes to \(\cos\) with a negative sign. Hence the answer is \(-\cos x\).
Step 3
Exam Tip
\(\frac{3\pi}{2}+x\) रूप में \(\sin\) बदलकर \(\cos\) होता है और चिन्ह ऋणात्मक होता है। इसलिए उत्तर \(-\cos x\) है।
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(\tan\(2\pi-x\)) किसके बराबर है?
What is (\tan\(2\pi-x\)) equal to?
#allied-angles
#tangent
#quadrants
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
In the fourth quadrant, \(\tan x\) is negative. Therefore, (\tan\(2\pi-x\)=-\tan x).
Step 2
Why this answer is correct
The correct answer is B. -\(\tan x\). In the fourth quadrant, \(\tan x\) is negative. Therefore, (\tan\(2\pi-x\)=-\tan x).
Step 3
Exam Tip
चौथे चतुर्थांश में \(\tan x\) ऋणात्मक होता है। इसलिए (\tan\(2\pi-x\)=-\tan x)।
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(\cos\(2\pi-x\)) किसके बराबर है?
What is (\cos\(2\pi-x\)) equal to?
#allied-angles
#cosine
#quadrants
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
\(2\pi-x\) lies in the fourth quadrant and \(\cos x\) remains positive. Hence (\cos\(2\pi-x\)=\cos x).
Step 2
Why this answer is correct
The correct answer is C. \(\cos x\). \(2\pi-x\) lies in the fourth quadrant and \(\cos x\) remains positive. Hence (\cos\(2\pi-x\)=\cos x).
Step 3
Exam Tip
\(2\pi-x\) चौथे चतुर्थांश में आता है और \(\cos x\) धनात्मक रहता है। इसलिए (\cos\(2\pi-x\)=\cos x)।
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(\sin\(2\pi-x\)) किसके बराबर है?
What is (\sin\(2\pi-x\)) equal to?
#allied-angles
#sine
#quadrants
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
\(2\pi-x\) is related to the fourth quadrant. There \(\sin x\) is negative, so (\sin\(2\pi-x\)=-\sin x).
Step 2
Why this answer is correct
The correct answer is B. -\(\sin x\). \(2\pi-x\) is related to the fourth quadrant. There \(\sin x\) is negative, so (\sin\(2\pi-x\)=-\sin x).
Step 3
Exam Tip
\(2\pi-x\) चौथे चतुर्थांश से संबंधित है। वहाँ \(\sin x\) ऋणात्मक होता है, इसलिए (\sin\(2\pi-x\)=-\sin x)।
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(\cos\(\frac{\pi}{2}+x\)) किसके बराबर है?
What is (\cos\(\frac{\pi}{2}+x\)) equal to?
#cofunction-identities
#cosine
#allied-angles
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
In the form \(\frac{\pi}{2}+x\), \(\cos\) changes to \(\sin\) with a negative sign. Hence it becomes \(-\sin x\).
Step 2
Why this answer is correct
The correct answer is B. \(-\sin x\). In the form \(\frac{\pi}{2}+x\), \(\cos\) changes to \(\sin\) with a negative sign. Hence it becomes \(-\sin x\).
Step 3
Exam Tip
\(\frac{\pi}{2}+x\) वाले रूप में \(\cos\) बदलकर \(\sin\) होता है और चिन्ह ऋणात्मक होता है। इसलिए \(-\sin x\) मिलता है।
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(\sin\(\frac{\pi}{2}+x\)) किसके बराबर है?
What is (\sin\(\frac{\pi}{2}+x\)) equal to?
#cofunction-identities
#sine
#allied-angles
A \(-\cos x\)
B \(\sin x\)
C \(-\sin x\)
D \(\cos x\)
Explanation opens after your attempt
Correct Answer
D. \(\cos x\)
Step 1
Concept
In the form \(\frac{\pi}{2}+x\), \(\sin\) changes to \(\cos\) and the sign remains positive. Hence the answer is \(\cos x\).
Step 2
Why this answer is correct
The correct answer is D. \(\cos x\). In the form \(\frac{\pi}{2}+x\), \(\sin\) changes to \(\cos\) and the sign remains positive. Hence the answer is \(\cos x\).
Step 3
Exam Tip
\(\frac{\pi}{2}+x\) वाले रूप में \(\sin\) बदलकर \(\cos\) होता है और चिन्ह धनात्मक रहता है। इसलिए उत्तर \(\cos x\) है।
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(\tan\(\pi+x\)-\tan\(\pi-x\)) का सरल मान क्या है?
What is the simplified value of (\tan\(\pi+x\)-\tan\(\pi-x\))?
#allied-angles
#tangent
#simplification
A (0)
B \(-2\tan x\)
C \(2\tan x\)
D \(\tan x\)
Explanation opens after your attempt
Correct Answer
C. \(2\tan x\)
Step 1
Concept
(\tan\(\pi+x\)=\tan x) and (\tan\(\pi-x\)=-\tan x). Therefore, the difference is \(2\tan x\).
Step 2
Why this answer is correct
The correct answer is C. \(2\tan x\). (\tan\(\pi+x\)=\tan x) and (\tan\(\pi-x\)=-\tan x). Therefore, the difference is \(2\tan x\).
Step 3
Exam Tip
(\tan\(\pi+x\)=\tan x) और (\tan\(\pi-x\)=-\tan x) होते हैं। इसलिए अंतर \(2\tan x\) है।
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(\cos\(\pi+x\)+\cos\(\pi-x\)) का सरल मान क्या है?
What is the simplified value of (\cos\(\pi+x\)+\cos\(\pi-x\))?
#allied-angles
#cosine
#simplification
A \(-2\cos x\)
B \(2\cos x\)
C (0)
D \(2\sin x\)
Explanation opens after your attempt
Correct Answer
A. \(-2\cos x\)
Step 1
Concept
(\cos\(\pi+x\)=-\cos x) and (\cos\(\pi-x\)=-\cos x). Therefore, the sum is \(-2\cos x\).
Step 2
Why this answer is correct
The correct answer is A. \(-2\cos x\). (\cos\(\pi+x\)=-\cos x) and (\cos\(\pi-x\)=-\cos x). Therefore, the sum is \(-2\cos x\).
Step 3
Exam Tip
(\cos\(\pi+x\)=-\cos x) और (\cos\(\pi-x\)=-\cos x) होते हैं। इसलिए योग \(-2\cos x\) है।
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(\sin\(\pi+x\)+\sin\(\pi-x\)) का सरल मान क्या है?
What is the simplified value of (\sin\(\pi+x\)+\sin\(\pi-x\))?
#allied-angles
#sine
#simplification
A \(2\sin x\)
B (0)
C \(-2\sin x\)
D \(2\cos x\)
Explanation opens after your attempt
Step 1
Concept
(\sin\(\pi+x\)=-\sin x) and (\sin\(\pi-x\)=\sin x). Hence the sum is (0).
Step 2
Why this answer is correct
The correct answer is B. (0). (\sin\(\pi+x\)=-\sin x) and (\sin\(\pi-x\)=\sin x). Hence the sum is (0).
Step 3
Exam Tip
(\sin\(\pi+x\)=-\sin x) और (\sin\(\pi-x\)=\sin x) होते हैं। इसलिए योग (0) है।
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(\cos\(\pi+x\)) किसके बराबर है?
What is (\cos\(\pi+x\)) equal to?
#allied-angles
#cosine
#quadrants
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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(\sin\(\pi+x\)) किसके बराबर है?
What is (\sin\(\pi+x\)) equal to?
#allied-angles
#sine
#quadrants
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 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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(\tan\(\pi+x\)) किसके बराबर है?
What is (\tan\(\pi+x\)) equal to?
#periodicity
#tangent
#allied-angles
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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(\cos\(\pi-x\)) किसके बराबर है?
What is (\cos\(\pi-x\)) equal to?
#trigonometric-properties
#allied-angles
#cosine
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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(\sin\(\pi-x\)) किसके बराबर है?
What is (\sin\(\pi-x\)) equal to?
#trigonometric-properties
#allied-angles
#sine
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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