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Question: If \(\int_{}^{}\frac{f(x)dx}{{logsin}x}\) = log log sin x, then f(x) =...

If ∫f(x)dxlogsinx\int_{}^{}\frac{f(x)dx}{{logsin}x} = log log sin x, then f(x) =

A

sin x

B

cos x

C

log sin x

D

cot x

Answer

cot x

Explanation

Solution

= log log sinx

Differentiating both sides, we get

f(x)log⁡sin⁡x\frac { f ( x ) } { \log \sin x } = cot⁡xlogsinx\frac{\cot x}{{logsin}x} Ž f(x) = cotx.