If sin ^{-1} x + sin ^{-1} y = frac{pi}{2},th | vedclass

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(A) Given that,$\sin ^{-1} x + \sin ^{-1} y = \frac{\pi}{2} \dots (1)$ We know the identity $\sin ^{-1} x + \cos ^{-1} x = \frac{\pi}{2} \dots (2)$ Co

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$1 - y^{2}$

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(A) Given that,$\sin ^{-1} x + \sin ^{-1} y = \frac{\pi}{2} \dots (1)$ We know the identity $\sin ^{-1} x + \cos ^{-1} x = \frac{\pi}{2} \dots (2)$ Comparing equations $(1)$ and $(2)$,we get $\sin ^{-1} y = \cos ^{-1} x$ Taking $\cos$ on both sides,we have $\cos(\sin ^{-1} y) = \cos(\cos ^{-1} x)$ Since $\cos(\sin ^{-1} y) = \sqrt{1 - y^{2}}$,we get $x = \sqrt{1 - y^{2}}$ Squaring both sides,we obtain $x^{2} = 1 - y^{2}$

If $\sin ^{-1} x + \sin ^{-1} y = \frac{\pi}{2}$,then $x^{2}$ is equal to

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