Question

If `("f"(x))/(log (sec x)) "dx"` = log(log sec x) + c, then f(x) = ______.

Options

• cot x

• tan x

• sec x

• cosec x

Answer 1

If `("f"(x))/(log (sec x)) "dx"` = log(log sec x) + c, then f(x) = tan x.

Explanation:

`int ("f"(x))/(log (sec x)) "dx"` = log(log sec x) + c

Differentiating on both sides, we get

`("f"(x))/(log (sec x)) = 1/(log (sec x)) xx 1/(sec x) xx sec x * tan x`

`("f"(x))/(log (sec x)) = (tan x)/(log (sec x))`

`=> "f"(x) = tan x`