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If $\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2}$, then $\cos ^{-1} x+\cos ^{-1} y$ is equal to
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The correct answer is:
$\frac{\pi}{2}$
Given $\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2}$
we know that $\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}$
$\begin{array}{l}
\Rightarrow \sin ^{-1} x=\pi / 2-\cos ^{-1} x \\
\therefore \text { Equation (1) becomes. }
\end{array}$
$\frac{\pi}{2}-\cos ^{-1} x+\frac{\pi}{2}-\cos ^{-1} y=\frac{\pi}{2}$
$\Rightarrow \cos ^{-1} x+\cos ^{-1} y=\frac{\pi}{2}$
we know that $\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}$
$\begin{array}{l}
\Rightarrow \sin ^{-1} x=\pi / 2-\cos ^{-1} x \\
\therefore \text { Equation (1) becomes. }
\end{array}$
$\frac{\pi}{2}-\cos ^{-1} x+\frac{\pi}{2}-\cos ^{-1} y=\frac{\pi}{2}$
$\Rightarrow \cos ^{-1} x+\cos ^{-1} y=\frac{\pi}{2}$
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