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If int(f(x))/(log(sinx))dx=log[log sinx]...

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

A

`cot x`

B

`tanx`

C

`sec x`

D

`"cosec x"`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `int(f(x))/(log(sinx))dx=log[logsinx]+c`
On differentiating both sides, we get
`(f(x))/(log(sinx))=(1)/(log sinx)(d)/(dx)(log sinx)+0`
`rArr" "(f(x))/(log(sinx))=(1)/(log sinx)xx(1)/(sinx)xx(1)/(sinx)xxcosx`
`rArr" "f(x)=cotx`
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