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Minimum value of (sin^(-1)x)^(2)+(cos^(-...

Minimum value of `(sin^(-1)x)^(2)+(cos^(-1)x)^(2)` is greater than

A

`(pi^(2))/4`

B

`(pi^(2))/16`

C

`(3pi^(2))/4`

D

`(3pi^(2))/32`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`(sin^(-1)x)^(2)+((pi)/2-sin^(-1)x)^(2)=t^(2)+((pi)/2-t)^(2)` where `sin^(-1)x=t`
`=2t^(2)-pit+(pi^(2))/4` is minimum when `t=(pi)/4`
Minimum value `=(pi^(2))/8`
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