1.

If `int(f(x))/(log(sinx))dx=log[log sinx]+c`, then f(x) is equal toA. `cot x`B. `tanx`C. `sec x`D. `"cosec x"`

Answer» Correct Answer - 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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