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Minimum value of `(sin^(-1)x)^(2)+(cos^(-1)x)^(2)` is greater thanA. `(pi^(2))/4`B. `(pi^(2))/16`C. `(3pi^(2))/4`D. `(3pi^(2))/32` |
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Answer» Correct Answer - 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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