Concept-wise Practice

half-angle MCQ Questions for Class 11

half-angle se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

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4 questions tagged with half-angle.

Question 1/4 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

\(\frac{1+\cos x}{\sin x}\) किसके बराबर है?

What is \(\frac{1+\cos x}{\sin x}\) equal to?

Explanation opens after your attempt
Correct Answer

C. \(\cot \frac{x}{2}\)

Step 1

Concept

The standard half-angle form is \(\cot \frac{x}{2}=\frac{1+\cos x}{\sin x}\). Keep the forms of \(\tan \frac{x}{2}\) and \(\cot \frac{x}{2}\) separate.

Step 2

Why this answer is correct

The correct answer is C. \(\cot \frac{x}{2}\). The standard half-angle form is \(\cot \frac{x}{2}=\frac{1+\cos x}{\sin x}\). Keep the forms of \(\tan \frac{x}{2}\) and \(\cot \frac{x}{2}\) separate.

Step 3

Exam Tip

मानक अर्ध-कोण रूप \(\cot \frac{x}{2}=\frac{1+\cos x}{\sin x}\) है। \(\tan \frac{x}{2}\) और \(\cot \frac{x}{2}\) के रूप अलग रखें।

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Question 2/4 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

\(\frac{\sin x}{1-\cos x}\) किसके बराबर है?

What is \(\frac{\sin x}{1-\cos x}\) equal to?

Explanation opens after your attempt
Correct Answer

B. \(\cot \frac{x}{2}\)

Step 1

Concept

By the half-angle identity, \(\frac{\sin x}{1-\cos x}=\cot \frac{x}{2}\). In such forms, identify the denominator carefully.

Step 2

Why this answer is correct

The correct answer is B. \(\cot \frac{x}{2}\). By the half-angle identity, \(\frac{\sin x}{1-\cos x}=\cot \frac{x}{2}\). In such forms, identify the denominator carefully.

Step 3

Exam Tip

अर्ध-कोण पहचान से \(\frac{\sin x}{1-\cos x}=\cot \frac{x}{2}\) होता है। ऐसे रूपों में हर देखकर पहचान करें।

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Question 3/4 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\frac{\sin x}{1+\cos x}\) किसके बराबर है?

What is \(\frac{\sin x}{1+\cos x}\) equal to?

Explanation opens after your attempt
Correct Answer

B. \(\tan \frac{x}{2}\)

Step 1

Concept

The standard half-angle identity is \(\tan \frac{x}{2}=\frac{\sin x}{1+\cos x}\). Identify the half-angle form quickly.

Step 2

Why this answer is correct

The correct answer is B. \(\tan \frac{x}{2}\). The standard half-angle identity is \(\tan \frac{x}{2}=\frac{\sin x}{1+\cos x}\). Identify the half-angle form quickly.

Step 3

Exam Tip

मानक अर्ध कोण पहचान \(\tan \frac{x}{2}=\frac{\sin x}{1+\cos x}\) है। ऐसे रूप में अर्ध कोण तुरंत पहचानें।

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Question 4/4 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\frac{1-\cos x}{1+\cos x}\) किसके बराबर है?

What is \(\frac{1-\cos x}{1+\cos x}\) equal to?

Explanation opens after your attempt
Correct Answer

C. \(\tan^2 \frac{x}{2}\)

Step 1

Concept

By the half-angle identity, \(\tan^2 \frac{x}{2}=\frac{1-\cos x}{1+\cos x}\). Remember half-angle forms separately.

Step 2

Why this answer is correct

The correct answer is C. \(\tan^2 \frac{x}{2}\). By the half-angle identity, \(\tan^2 \frac{x}{2}=\frac{1-\cos x}{1+\cos x}\). Remember half-angle forms separately.

Step 3

Exam Tip

अर्ध कोण पहचान के अनुसार \(\tan^2 \frac{x}{2}=\frac{1-\cos x}{1+\cos x}\)। अर्ध कोण रूपों को अलग से याद रखें।

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