1.

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

Answer» Correct Answer - `(pi)/(4) (pi + 2)`
`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)`


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