find the maximum value of `f(x) = (sin^(-1) (sin x))^(2) - sin^(-1) (sin x)`

Answer

`(pi)/(4) (pi + 2)`

Explanation

`f(x) = (sin^(-1) (sin x))^(2) - sin^(-1) (sin x)`
`= (sin^(-1) (sin x) - (1)/(3))^(2) - (1)/(4)`
For maximum value of `f(x), sin^(-1) (sinx) = (-pi)/(2)`
`:. F_("max") = (-(pi)/(2) -(1)/(2))^(2) - (1)/(4) = (pi)/(4) (pi + 2)`