Question

If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.

Options

• cot x

• tan x

• sec x

• cosec x

Answer 1

If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to cot x.

Explanation:

Since, `int (f(x))/(log(sin x))dx` = log[log sin x] + c

After differentiating on both sides, we get

`(f(x))/(log(sin x)) = 1/(logsinx)  d/dx(log sin x) + 0`

`\implies (f(x))/(log(sin x)) = 1/(log sin x) xx 1/sinx xx cosx`

`\implies` f(x) = cot x