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Maximum value of function f(x)=(sin^(-1)...

Maximum value of function `f(x)=(sin^(-1)(sinx)^(2)-sin^(-1)(sinx)` is:

A

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

B

`(pi)/(4)[pi-2]`

C

`(pi)/(2)[pi+2]`

D

`(pi)/(2)[pi-2]`

Text Solution

Verified by Experts

The correct Answer is:
A
`y=(sin^(-2)(sin x))^(2)-sin^(-1)(sin x)`
`=(sin^(-1)(sin x)-(1)/(2))^(2)-(1)/(4)`
For maximum value of `y, sin^(-1)(sin x)=-(pi)/(2)`
`rArr y =((pi)/(2)+(1)/(2))^(2)-(1)/(4)=(pi)/(4)(pi+2)`
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