If y = log (sin x), then $\frac{d^2 y}{d

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Continuity and Differentiability

Question:

If y = log (sin x), then $\frac{d^2 y}{d x^2}$ is :

Options:

–cosec²x

sec²x

–cosec x cot x

sec x tan x

Correct Answer:

–cosec²x

Explanation:

$y = \log (\sin x) \Rightarrow \frac{d y}{d x}=\frac{\cos x}{\sin x}=\cot x$

$\Rightarrow \frac{d^2 y}{d x^2}=-cosec^2 x$

Hence (1) is correct answer.