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If $4 \sin ^{-1} x+\cos ^{-1} x=\pi$, then $x$ is equal to
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Verified Answer
The correct answer is:
$\frac{1}{2}$
We know that $4 \sin ^{-1} x+\cos ^{-1} x=\pi$
$\begin{aligned}
& \Rightarrow 3 \sin ^{-1} x+\sin ^{-1} x+\cos ^{-1} x=\pi \\
& \Rightarrow 3 \sin ^{-1} x=\pi-\frac{\pi}{2}=\frac{\pi}{2} \\
& \Rightarrow \sin ^{-1} x=\pi / 6 \Rightarrow x=\sin \frac{\pi}{6}=\frac{1}{2} .
\end{aligned}$
$\begin{aligned}
& \Rightarrow 3 \sin ^{-1} x+\sin ^{-1} x+\cos ^{-1} x=\pi \\
& \Rightarrow 3 \sin ^{-1} x=\pi-\frac{\pi}{2}=\frac{\pi}{2} \\
& \Rightarrow \sin ^{-1} x=\pi / 6 \Rightarrow x=\sin \frac{\pi}{6}=\frac{1}{2} .
\end{aligned}$
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