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Mathematics Trigonometric functions and their properties MCQ Questions for Class 11

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Trigonometric functions and their properties Practice Questions

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Question 271/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cos \theta=\cos \alpha\), तो सामान्य हल कौन सा है?

If \(\cos \theta=\cos \alpha\), which is the general solution?

Explanation opens after your attempt
Correct Answer

B. \(\theta=2n\pi\pm\alpha\)

Explanation

Simple Explanation

\(\cos \theta=\cos \alpha\) के लिए दोनों दिशाओं में कोण मिलते हैं। परीक्षा में \(\pm\alpha\) लगाना न भूलें। / For \( \cos \theta=\cos \alpha\), angles occur in both directions. In exams do not forget \( \pm\alpha\).

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Question 272/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\tan \theta=\tan \alpha\), तो सामान्य हल क्या है?

If \(\tan \theta=\tan \alpha\), what is the general solution?

Explanation opens after your attempt
Correct Answer

B. \(\theta=n\pi+\alpha\)

Explanation

Simple Explanation

\(\tan \theta\) का period \(\pi\) है इसलिए हल \(\theta=n\pi+\alpha\) होगा। परीक्षा में tangent equations में \(\pi\) period लगाएं। / The period of \( \tan \theta\) is \( \pi\), so the solution is \( \theta=n\pi+\alpha\). In exams use period \( \pi\) for tangent equations.

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Question 273/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\tan\left(\frac{\pi}{2}-\theta\right)\) का मान क्या है?

What is the value of \(\tan\left(\frac{\pi}{2}-\theta\right)\)?

Explanation opens after your attempt
Correct Answer

C. \(\cot \theta\)

Explanation

Simple Explanation

\(\frac{\pi}{2}-\theta\) पर tangent का co-function cotangent होता है। परीक्षा में complementary angle property याद रखें। / At \( \frac{\pi}{2}-\theta\), tangent changes to its co-function cotangent. In exams remember complementary angle property.

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Question 274/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\cot\left(\frac{\pi}{2}-\theta\right)\) किसके बराबर है?

What is \(\cot\left(\frac{\pi}{2}-\theta\right)\) equal to?

Explanation opens after your attempt
Correct Answer

D. \(\tan \theta\)

Explanation

Simple Explanation

\(\frac{\pi}{2}-\theta\) पर cotangent का co-function tangent होता है। परीक्षा में reciprocal function pair याद रखें। / At \( \frac{\pi}{2}-\theta\), cotangent changes to the co-function tangent. In exams remember reciprocal function pairs.

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Question 275/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\sin \theta=\cos \theta\) और \(0<\theta<\frac{\pi}{2}\), तो \(\theta\) का मान क्या है?

If \(\sin \theta=\cos \theta\) and \(0<\theta<\frac{\pi}{2}\), what is the value of \(\theta\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{\pi}{4}\)

Explanation

Simple Explanation

\(\sin \theta=\cos \theta\) से \(\tan \theta=1\) और प्रथम चतुर्थांश में \(\theta=\frac{\pi}{4}\) है। परीक्षा में दोनों तरफ \(\cos \theta\) से भाग तभी दें जब वह शून्य न हो। / From \( \sin \theta=\cos \theta\), \( \tan \theta=1\), and in the first quadrant \( \theta=\frac{\pi}{4}\). In exams divide by \( \cos \theta\) only when it is nonzero.

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Question 276/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\sin \theta=\frac{1}{2}\) और \(0<\theta<\pi\), तो \(\theta\) के मान कौन से हैं?

If \(\sin \theta=\frac{1}{2}\) and \(0<\theta<\pi\), what are the values of \(\theta\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{\pi}{6},\frac{5\pi}{6}\)

Explanation

Simple Explanation

\(\sin \theta=\frac{1}{2}\) के reference angle \(\frac{\pi}{6}\) हैं और sine प्रथम व द्वितीय चतुर्थांश में धनात्मक है। परीक्षा में दिए interval में ही उत्तर चुनें। / The reference angle for \( \sin \theta=\frac{1}{2}\) is \( \frac{\pi}{6}\), and sine is positive in the first and second quadrants. In exams choose only answers in the given interval.

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Question 277/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cos \theta=\frac{1}{2}\) और \(0<\theta<2\pi\), तो \(\theta\) के मान कौन से हैं?

If \(\cos \theta=\frac{1}{2}\) and \(0<\theta<2\pi\), what are the values of \(\theta\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{\pi}{3},\frac{5\pi}{3}\)

Explanation

Simple Explanation

\(\cos \theta=\frac{1}{2}\) के लिए reference angle \(\frac{\pi}{3}\) है और cosine प्रथम व चतुर्थ चतुर्थांश में धनात्मक है। परीक्षा में \(2\pi\) तक के दोनों हल लिखें। / For \( \cos \theta=\frac{1}{2}\), the reference angle is \( \frac{\pi}{3}\), and cosine is positive in the first and fourth quadrants. In exams write both solutions up to \(2\pi\).

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Question 278/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\tan \theta=\sqrt{3}\) और \(0<\theta<\pi\), तो \(\theta\) का मान क्या होगा?

If \(\tan \theta=\sqrt{3}\) and \(0<\theta<\pi\), what is the value of \(\theta\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

\(\tan \theta=\sqrt{3}\) का reference angle \(\frac{\pi}{3}\) है और \(0<\theta<\pi\) में tangent प्रथम चतुर्थांश में धनात्मक है। परीक्षा में sign के अनुसार quadrant चुनें। / The reference angle for \( \tan \theta=\sqrt{3}\) is \( \frac{\pi}{3}\), and in \(0<\theta<\pi\) tangent is positive in the first quadrant. In exams choose the quadrant by sign.

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Question 279/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\frac{1-\cos^2 \theta}{\sin^2 \theta}\) का सरल मान क्या है, जब \(\sin \theta\neq0\)?

What is the simplified value of \(\frac{1-\cos^2 \theta}{\sin^2 \theta}\), when \(\sin \theta\neq0\)?

Explanation opens after your attempt
Correct Answer

B. (1)

Explanation

Simple Explanation

क्योंकि \(1-\cos^2 \theta=\sin^2 \theta\), इसलिए अनुपात (1) है। परीक्षा में denominator condition जरूर देखें। / Because \(1-\cos^2 \theta=\sin^2 \theta\), the ratio is (1). In exams always check the denominator condition.

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Question 280/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\frac{1-\sin^2 \theta}{\cos^2 \theta}\) का सरल मान क्या है, जब \(\cos \theta\neq0\)?

What is the simplified value of \(\frac{1-\sin^2 \theta}{\cos^2 \theta}\), when \(\cos \theta\neq0\)?

Explanation opens after your attempt
Correct Answer

C. (1)

Explanation

Simple Explanation

क्योंकि \(1-\sin^2 \theta=\cos^2 \theta\), इसलिए मान (1) होगा। परीक्षा में basic identity से numerator बदलें। / Because \(1-\sin^2 \theta=\cos^2 \theta\), the value is (1). In exams replace the numerator using the basic identity.

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