If sin^{-1} x + sin^{-1} y = pi/2, then x^2 i | vedclass

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(A) Given $\sin^{-1} x + \sin^{-1} y = \pi/2$.We know that $\sin^{-1} y + \cos^{-1} y = \pi/2$, so $\sin^{-1} y = \pi/2 - \cos^{-1} y$.Substituting th

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$1 - y^2$

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(A) Given $\sin^{-1} x + \sin^{-1} y = \pi/2$.We know that $\sin^{-1} y + \cos^{-1} y = \pi/2$, so $\sin^{-1} y = \pi/2 - \cos^{-1} y$.Substituting this into the given equation: $\sin^{-1} x = \pi/2 - \sin^{-1} y = \cos^{-1} y$.Taking $\sin$ on both sides: $x = \sin(\cos^{-1} y)$.Using the identity $\sin(\cos^{-1} y) = \sqrt{1 - y^2}$, we get $x = \sqrt{1 - y^2}$.Squaring both sides, we get $x^2 = 1 - y^2$.

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

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