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If $\sin ^{-1} x=\frac{\pi}{5}$ for some $x \in(-1,1)$, then the value of $\cos ^{-1} x$ is
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$\frac{3 \pi}{10}$
$\begin{aligned} & \sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2} \\ & \Rightarrow \cos ^{-1} x=\frac{\pi}{2}-\sin ^{-1} x=\frac{\pi}{2}-\frac{\pi}{5}=\frac{3 \pi}{10}\end{aligned}$
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