Question:
$\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1$
Solution:
$\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1$
$\Rightarrow \sin ^{-1} \frac{1}{5}+\cos ^{-1} x=\sin ^{-1} 1$
$\Rightarrow \sin ^{-1} \frac{1}{5}+\cos ^{-1} x=\frac{\pi}{2}$
$\Rightarrow \sin ^{-1} \frac{1}{5}=\frac{\pi}{2}-\cos ^{-1} x$
$\Rightarrow \sin ^{-1} \frac{1}{5}=\sin ^{-1} x$ $\left[\because \sin ^{-1} x=\frac{\pi}{2}-\cos ^{-1} x\right]$
$\Rightarrow x=\frac{1}{5}$
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