What will be the value of cos x cosec x

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

What will be the value of cos x cosec x - sin x sec x ?

Options:

cot $\frac{2x}{2}$

tan 2x

cot 2x

2 cot 2x

Correct Answer:

2 cot 2x

Explanation:

Given :-

cos x cosec x - sin x sec x

= $\frac{cosx}{sinx}$ - $\frac{sinx}{cosx}$

= $\frac{cos²x - sin²x}{sinx . cosx}$

Multiply and divide by 2

= 2 × $\frac{cos²x - sin²x}{2 .sinx . cosx}$

= 2 × $\frac{cos2x}{sin2x}$

= 2 cot2x