If `int(f(x))/(logsinx)dx=log*logsinx,` then f(x) is equal to

Options

A. cot x
B. tan x
C. sec x
D. cosec x

Answer

A

Explanation

Given `int (f(x))/(log (sin x))dx=log [log sin x]+c`
On differentiating both sides, we get
`(f(x))/(log(sin x))=(1)/(log sinx) (d)/(dx) (log sin x)+0`
`Rightarrow (f(x))/(log(sinx))=(1)/(log sin x)xx (1)/(sin x) xx cos x`
`Rightarrow f(x)=cot x`