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If $\cos ^{-1} x+\cos ^{-1} y=2 \pi$, then $\sin ^{-1} x+\sin ^{-1} y$ is equal to
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The correct answer is:
$-\pi$
$\begin{aligned} & \cos ^{-1} x+\cos ^{-1} y=2 \pi \\ & \Rightarrow \frac{\pi}{2}-\sin ^{-1} x+\frac{\pi}{2}-\sin ^{-1} y=2 \pi \\ & \Rightarrow \pi-\left(\sin ^{-1} x+\sin ^{-1} y\right)=2 \pi \\ & \Rightarrow \sin ^{-1} x+\sin ^{-1} y=-\pi\end{aligned}$
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