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

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Trigonometric functions and their properties Practice Questions

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Question 301/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\tan \theta+\cot \theta=4\), तो \(\tan^2\theta+\cot^2\theta\) का मान क्या है?

If \(\tan \theta+\cot \theta=4\), what is the value of \(\tan^2\theta+\cot^2\theta\)?

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Correct Answer

A. (14)

Explanation

Simple Explanation

(\(\tan \theta+\cot \theta\)2=\tan-2\theta+\cot-2\theta+2) होता है। इसलिए मान (16-2=14) है। / We use (\(\tan \theta+\cot \theta\)2=\tan-2\theta+\cot-2\theta+2). Hence the value is (16-2=14).

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Question 302/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\sin^2 20^\circ+\sin^2 70^\circ\) का मान क्या है?

What is the value of \(\sin^2 20^\circ+\sin^2 70^\circ\)?

Explanation opens after your attempt
Correct Answer

B. (1)

Explanation

Simple Explanation

क्योंकि \(\sin 70^\circ=\cos 20^\circ\), इसलिए योग \(\sin^2 20^\circ+\cos^2 20^\circ=1\) है। परीक्षा में complementary angles पहचानें। / Since \(\sin 70^\circ=\cos 20^\circ\), the sum is \(\sin^2 20^\circ+\cos^2 20^\circ=1\). In exams, identify complementary angles.

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Question 303/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

फलन (f(x)=\tan\frac{x}{2}+\cot\frac{x}{2}) का मूल आवर्त क्या है?

What is the fundamental period of (f(x)=\tan\frac{x}{2}+\cot\frac{x}{2})?

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Correct Answer

C. \( 2\pi \)

Explanation

Simple Explanation

\(\tan\frac{x}{2}\) और \(\cot\frac{x}{2}\) दोनों का आवर्त \(2\pi\) है। परीक्षा में \(\tan ax\) का आवर्त \( \frac{\pi}{|a|} \) लगाएं। / Both \(\tan\frac{x}{2}\) and \(\cot\frac{x}{2}\) have period \(2\pi\). In exams, use the period of \(\tan ax\) as \( \frac{\pi}{|a|} \).

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Question 304/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

फलन (f(x)=\sin x+\cos x) का परिसर क्या है?

What is the range of (f(x)=\sin x+\cos x)?

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Correct Answer

D. \( [-\sqrt{2},\sqrt{2}] \)

Explanation

Simple Explanation

(\sin x+\cos x=\sqrt{2}\sin\left\(x+\frac{\pi}{4}\right\)) होता है। इसलिए परिसर \( [-\sqrt{2},\sqrt{2}] \) है। / We have (\sin x+\cos x=\sqrt{2}\sin\left\(x+\frac{\pi}{4}\right\)). Hence the range is \( [-\sqrt{2},\sqrt{2}] \).

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Question 305/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

फलन (f(x)=\sin x\cos x) किस प्रकार का है?

What type of function is (f(x)=\sin x\cos x)?

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Correct Answer

B. विषम फलनOdd function

Explanation

Simple Explanation

(f(-x)=\sin(-x)\cos(-x)=-\sin x\cos x=-f(x)) है। इसलिए यह विषम फलन है। / Here (f(-x)=\sin(-x)\cos(-x)=-\sin x\cos x=-f(x)). So it is an odd function.

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Question 306/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\sin x=\frac{3}{5}\) और (x) प्रथम चतुर्थांश में है, तो \(\tan x\) का मान क्या है?

If \(\sin x=\frac{3}{5}\) and (x) lies in the first quadrant, what is the value of \(\tan x\)?

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Correct Answer

A. \( \frac{3}{4} \)

Explanation

Simple Explanation

\(\cos x=\frac{4}{5}\) होगा, इसलिए \(\tan x=\frac{\sin x}{\cos x}=\frac{3}{4}\)। परीक्षा में चतुर्थांश से चिन्ह तय करें। / We get \(\cos x=\frac{4}{5}\), so \(\tan x=\frac{\sin x}{\cos x}=\frac{3}{4}\). In exams, decide the sign from the quadrant.

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Question 307/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

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

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

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Correct Answer

C. \(\cos x\)

Explanation

Simple Explanation

\(\frac{\pi}{2}+x\) के लिए sine, cosine में बदलता है और दूसरे चतुर्थांश में धनात्मक रहता है। इसलिए मान \(\cos x\) है। / For \(\frac{\pi}{2}+x\), sine changes to cosine and remains positive in the second quadrant. Hence the value is \(\cos x\).

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Question 308/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\cos\(\pi+x\)) का सही सरलीकृत रूप क्या है?

What is the correct simplified form of (\cos\(\pi+x\))?

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Correct Answer

D. \(-\cos x\)

Explanation

Simple Explanation

\(\pi+x\) तीसरे चतुर्थांश से जुड़ा रूप है जहाँ \(\cos x\) ऋणात्मक होता है। इसलिए (\cos\(\pi+x\)=-\cos x)। / The form \(\pi+x\) is linked to the third quadrant where \(\cos x\) is negative. Hence (\cos\(\pi+x\)=-\cos x).

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Question 309/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\tan x=2\), तो \(\frac{1-\tan^2 x}{1+\tan^2 x}\) का मान क्या है?

If \(\tan x=2\), what is the value of \(\frac{1-\tan^2 x}{1+\tan^2 x}\)?

Explanation opens after your attempt
Correct Answer

A. \( -\frac{3}{5} \)

Explanation

Simple Explanation

सीधा रखने पर \(\frac{1-4}{1+4}=-\frac{3}{5}\) मिलता है। यह \(\cos 2x\) का भी रूप है। / Direct substitution gives \(\frac{1-4}{1+4}=-\frac{3}{5}\). This is also the form of \(\cos 2x\).

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Question 310/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\sin x+\sin 3x\) का गुणनफल रूप क्या है?

What is the product form of \(\sin x+\sin 3x\)?

Explanation opens after your attempt
Correct Answer

A. \(2\sin 2x\cos x\)

Explanation

Simple Explanation

सूत्र \(\sin A+\sin B=2\sin\frac{A+B}{2}\cos\frac{A-B}{2}\) लगाएं। यहाँ उत्तर \(2\sin 2x\cos x\) है। / Use \(\sin A+\sin B=2\sin\frac{A+B}{2}\cos\frac{A-B}{2}\). Here the answer is \(2\sin 2x\cos x\).

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