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  4. ( sin -1 x)2+( sin -1 y)2+2( sin -1 x)( sin -1 y)=π2, then x2+y2 is equal to -

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Q. $\left(\sin ^{-1} x\right)^2+\left(\sin ^{-1} y\right)^2+2\left(\sin ^{-1} x\right)\left(\sin ^{-1} y\right)=\pi^2$, then $x^2+y^2$ is equal to -

Inverse Trigonometric Functions

Solution:

$\left(\sin ^{-1} x+\sin ^{-1} y\right)^2=\pi^2$
$\Rightarrow \sin ^{-1} x+\sin ^{-1} y=\pm \pi$
$\Rightarrow \sin ^{-1} x=\sin ^{-1} y=\frac{\pi}{2}$
or $\sin ^{-1} x=\sin ^{-1} y=-\frac{\pi}{2}$
$\Rightarrow x^2+y^2=2$.