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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 221/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

\(\sec^2 x+\cosec^2 x\) को \(\tan x\) और \(\cot x\) के रूप में कैसे लिखा जा सकता है?

How can \(\sec^2 x+\cosec^2 x\) be written in terms of \(\tan x\) and \(\cot x\)?

Explanation opens after your attempt
Correct Answer

B. \(2+\tan^2 x+\cot^2 x\)

Explanation

Simple Explanation

\(\sec^2 x=1+\tan^2 x\) और \(\cosec^2 x=1+\cot^2 x\) लगाएँ। योग \(2+\tan^2 x+\cot^2 x\) होगा। / Use \(\sec^2 x=1+\tan^2 x\) and \(\cosec^2 x=1+\cot^2 x\). The sum becomes \(2+\tan^2 x+\cot^2 x\).

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Question 222/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

\(\frac{\tan x+\cot x}{\sec x\cosec x}\) का सरल मान क्या है?

What is the simplified value of \(\frac{\tan x+\cot x}{\sec x\cosec x}\)?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

\(\tan x+\cot x=\frac{1}{\sin x\cos x}\) और \(\sec x\cosec x=\frac{1}{\sin x\cos x}\) होता है। इसलिए अनुपात (1) है। / \(\tan x+\cot x=\frac{1}{\sin x\cos x}\) and \(\sec x\cosec x=\frac{1}{\sin x\cos x}\). Hence the ratio is (1).

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Question 223/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

\(\frac{\sec x}{\tan x}\) का सरल मान क्या है?

What is the simplified value of \(\frac{\sec x}{\tan x}\)?

Explanation opens after your attempt
Correct Answer

B. \(\cosec x\)

Explanation

Simple Explanation

\(\sec x=\frac{1}{\cos x}\) और \(\tan x=\frac{\sin x}{\cos x}\) रखें। अनुपात \(\frac{1}{\sin x}=\cosec x\) बनता है। / Put \(\sec x=\frac{1}{\cos x}\) and \(\tan x=\frac{\sin x}{\cos x}\). The ratio becomes \(\frac{1}{\sin x}=\cosec x\).

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Question 224/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

\(\frac{\cosec x}{\cot x}\) का सरल मान क्या है?

What is the simplified value of \(\frac{\cosec x}{\cot x}\)?

Explanation opens after your attempt
Correct Answer

B. \(\sec x\)

Explanation

Simple Explanation

\(\cosec x=\frac{1}{\sin x}\) और \(\cot x=\frac{\cos x}{\sin x}\) रखें। अनुपात \(\frac{1}{\cos x}=\sec x\) होगा। / Put \(\cosec x=\frac{1}{\sin x}\) and \(\cot x=\frac{\cos x}{\sin x}\). The ratio becomes \(\frac{1}{\cos x}=\sec x\).

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Question 225/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

(\sin-2 x\(1+\cot^2 x\)) का सरल मान क्या है?

What is the simplified value of (\sin-2 x\(1+\cot^2 x\))?

Explanation opens after your attempt
Correct Answer

B. (1)

Explanation

Simple Explanation

क्योंकि \(1+\cot^2 x=\cosec^2 x\)। इसलिए \(\sin^2 x\cosec^2 x=1\) होगा। / Since \(1+\cot^2 x=\cosec^2 x\). Therefore, \(\sin^2 x\cosec^2 x=1\).

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Question 226/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

(\cos-2 x\(1+\tan^2 x\)) का सरल मान क्या है?

What is the simplified value of (\cos-2 x\(1+\tan^2 x\))?

Explanation opens after your attempt
Correct Answer

C. (1)

Explanation

Simple Explanation

क्योंकि \(1+\tan^2 x=\sec^2 x\)। इसलिए \(\cos^2 x\sec^2 x=1\) है। / Since \(1+\tan^2 x=\sec^2 x\). Therefore, \(\cos^2 x\sec^2 x=1\).

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Question 227/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

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

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

Explanation opens after your attempt
Correct Answer

B. \(\frac{3}{5}\)

Explanation

Simple Explanation

\(\tan^2 x=\frac{1}{4}\) रखें। तब मान \(\frac{1-\frac{1}{4}}{1+\frac{1}{4}}=\frac{3}{5}\) है। / Put \(\tan^2 x=\frac{1}{4}\). Then the value is \(\frac{1-\frac{1}{4}}{1+\frac{1}{4}}=\frac{3}{5}\).

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Question 228/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

यदि \(\cot x=\frac{3}{2}\), तो \(\frac{\cot^2 x-1}{\cot^2 x+1}\) का मान क्या है?

If \(\cot x=\frac{3}{2}\), what is the value of \(\frac{\cot^2 x-1}{\cot^2 x+1}\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

\(\cot^2 x=\frac{9}{4}\) रखकर सरल करें। मान \(\frac{\frac{9}{4}-1}{\frac{9}{4}+1}=\frac{5}{13}\) है। / Substitute \(\cot^2 x=\frac{9}{4}\) and simplify. The value is \(\frac{\frac{9}{4}-1}{\frac{9}{4}+1}=\frac{5}{13}\).

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Question 229/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

\(\sin^4 x+\cos^4 x\) किसके बराबर है?

What is \(\sin^4 x+\cos^4 x\) equal to?

Explanation opens after your attempt
Correct Answer

B. \(1-2\sin^2 x\cos^2 x\)

Explanation

Simple Explanation

(\sin-4 x+\cos-4 x=\(\sin^2 x+\cos^2 x\)2-2\sin-2 x\cos-2 x) लिखें। पहला वर्ग (1) है। / Write (\sin-4 x+\cos-4 x=\(\sin^2 x+\cos^2 x\)2-2\sin-2 x\cos-2 x). The first square is (1).

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Question 230/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

यदि \(\sin x\cos x=\frac{1}{4}\), तो \(\sin^4 x+\cos^4 x\) का मान क्या है?

If \(\sin x\cos x=\frac{1}{4}\), what is the value of \(\sin^4 x+\cos^4 x\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{7}{8}\)

Explanation

Simple Explanation

पहचान \(\sin^4 x+\cos^4 x=1-2\sin^2 x\cos^2 x\) लगाएँ। \(\sin^2 x\cos^2 x=\frac{1}{16}\), इसलिए मान \(\frac{7}{8}\) है। / Use \(\sin^4 x+\cos^4 x=1-2\sin^2 x\cos^2 x\). Since \(\sin^2 x\cos^2 x=\frac{1}{16}\), the value is \(\frac{7}{8}\).

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