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Mathematics Trigonometric functions and their properties MCQ Questions for Class 11 General

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Question 161/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\cot x=\frac{5}{12}\) और (x) प्रथम चतुर्थांश में है, तो \(\cos x\) का मान क्या है?

If \(\cot x=\frac{5}{12}\) and (x) is in the first quadrant, what is the value of \(\cos x\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{5}{13}\)

Explanation

Simple Explanation

\(\cot x=\frac{5}{12}\) में आसन्न (5) और सामने (12) मानें। कर्ण (13) होगा, इसलिए \(\cos x=\frac{5}{13}\)। / For \(\cot x=\frac{5}{12}\), take adjacent as (5) and opposite as (12). The hypotenuse is (13), so \(\cos x=\frac{5}{13}\).

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Question 162/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\sin\(\pi+x\)+\sin\(\pi-x\)) का सरल मान क्या है?

What is the simplified value of (\sin\(\pi+x\)+\sin\(\pi-x\))?

Explanation opens after your attempt
Correct Answer

B. (0)

Explanation

Simple Explanation

(\sin\(\pi+x\)=-\sin x) और (\sin\(\pi-x\)=\sin x) होते हैं। इसलिए योग (0) है। / (\sin\(\pi+x\)=-\sin x) and (\sin\(\pi-x\)=\sin x). Hence the sum is (0).

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Question 163/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\cos\(\pi+x\)+\cos\(\pi-x\)) का सरल मान क्या है?

What is the simplified value of (\cos\(\pi+x\)+\cos\(\pi-x\))?

Explanation opens after your attempt
Correct Answer

A. \(-2\cos x\)

Explanation

Simple Explanation

(\cos\(\pi+x\)=-\cos x) और (\cos\(\pi-x\)=-\cos x) होते हैं। इसलिए योग \(-2\cos x\) है। / (\cos\(\pi+x\)=-\cos x) and (\cos\(\pi-x\)=-\cos x). Therefore, the sum is \(-2\cos x\).

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Question 164/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\tan\(\pi+x\)-\tan\(\pi-x\)) का सरल मान क्या है?

What is the simplified value of (\tan\(\pi+x\)-\tan\(\pi-x\))?

Explanation opens after your attempt
Correct Answer

C. \(2\tan x\)

Explanation

Simple Explanation

(\tan\(\pi+x\)=\tan x) और (\tan\(\pi-x\)=-\tan x) होते हैं। इसलिए अंतर \(2\tan x\) है। / (\tan\(\pi+x\)=\tan x) and (\tan\(\pi-x\)=-\tan x). Therefore, the difference is \(2\tan x\).

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Question 165/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\sin\(\frac{\pi}{2}+x\)) किसके बराबर है?

What is (\sin\(\frac{\pi}{2}+x\)) equal to?

Explanation opens after your attempt
Correct Answer

D. \(\cos x\)

Explanation

Simple Explanation

\(\frac{\pi}{2}+x\) वाले रूप में \(\sin\) बदलकर \(\cos\) होता है और चिन्ह धनात्मक रहता है। इसलिए उत्तर \(\cos x\) है। / In the form \(\frac{\pi}{2}+x\), \(\sin\) changes to \(\cos\) and the sign remains positive. Hence the answer is \(\cos x\).

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Question 166/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\cos\(\frac{\pi}{2}+x\)) किसके बराबर है?

What is (\cos\(\frac{\pi}{2}+x\)) equal to?

Explanation opens after your attempt
Correct Answer

B. \(-\sin x\)

Explanation

Simple Explanation

\(\frac{\pi}{2}+x\) वाले रूप में \(\cos\) बदलकर \(\sin\) होता है और चिन्ह ऋणात्मक होता है। इसलिए \(-\sin x\) मिलता है। / In the form \(\frac{\pi}{2}+x\), \(\cos\) changes to \(\sin\) with a negative sign. Hence it becomes \(-\sin x\).

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Question 167/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\tan\(\frac{\pi}{2}+x\)) किसके बराबर है?

What is (\tan\(\frac{\pi}{2}+x\)) equal to?

Explanation opens after your attempt
Correct Answer

A. \(-\cot x\)

Explanation

Simple Explanation

\(\frac{\pi}{2}+x\) पर \(\tan\) बदलकर \(\cot\) होता है और चिन्ह ऋणात्मक होता है। इसलिए (\tan\(\frac{\pi}{2}+x\)=-\cot x)। / At \(\frac{\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{\pi}{2}+x\)=-\cot x).

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Question 168/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\sec\(\frac{\pi}{2}-x\)) किसके बराबर है?

What is (\sec\(\frac{\pi}{2}-x\)) equal to?

Explanation opens after your attempt
Correct Answer

C. \(\cosec x\)

Explanation

Simple Explanation

(\cos\(\frac{\pi}{2}-x\)=\sin x), इसलिए (\sec\(\frac{\pi}{2}-x\)=\frac{1}{\sin x}=\cosec x)। पूरक कोण में सहफलन बनता है। / (\cos\(\frac{\pi}{2}-x\)=\sin x), so (\sec\(\frac{\pi}{2}-x\)=\frac{1}{\sin x}=\cosec x). Complementary angles give cofunctions.

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Question 169/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\cosec\(\frac{\pi}{2}-x\)) किसके बराबर है?

What is (\cosec\(\frac{\pi}{2}-x\)) equal to?

Explanation opens after your attempt
Correct Answer

A. \(\sec x\)

Explanation

Simple Explanation

(\sin\(\frac{\pi}{2}-x\)=\cos x), इसलिए (\cosec\(\frac{\pi}{2}-x\)=\frac{1}{\cos x}=\sec x)। व्युत्क्रम और पूरक पहचान साथ लगाएँ। / (\sin\(\frac{\pi}{2}-x\)=\cos x), so (\cosec\(\frac{\pi}{2}-x\)=\frac{1}{\cos x}=\sec x). Use reciprocal and cofunction identities together.

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Question 170/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि (x) दूसरे चतुर्थांश में है और \(\sin x=\frac{7}{25}\), तो \(\cos x\) का मान क्या है?

If (x) is in the second quadrant and \(\sin x=\frac{7}{25}\), what is the value of \(\cos x\)?

Explanation opens after your attempt
Correct Answer

C. \(-\frac{24}{25}\)

Explanation

Simple Explanation

पहचान से \(|\cos x|=\frac{24}{25}\) मिलता है। दूसरे चतुर्थांश में \(\cos x\) ऋणात्मक होता है। / The identity gives \(|\cos x|=\frac{24}{25}\). In the second quadrant, \(\cos x\) is negative.

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