If g (x) = `int_(0)^(x) ln(sec t tan t - sec^(2)t + 1)` dt , then set of value of x in `((-pi)/(2) , (pi)/(2))` for which g(x) is increasing , is

Options

A. `(-(pi)/(6) , (pi)/(6))`
B. `(0 , (pi)/(2))`
C. `(-(pi)/(2) , 0)`
D. `phi`

Answer

D

Explanation

g'(x) = ln (sec x tan x - `sec^(2)x + 1) ge0`
`implies` secx tan x - `sec^(2)x + 1 ge 1`
`implies (sinx - 1)/(cos^(2)x) ge 0`
`implies sin x- 1 ge 0 `