Question:
If $\cos \left(\sin ^{-1} \frac{2}{5}+\cos ^{-1} x\right)=0$, find the value of $x$
Solution:
$\cos \left(\sin ^{-1} \frac{2}{5}+\cos ^{-1} x\right)=0$
$\Rightarrow \cos \left(\sin ^{-1} \frac{2}{5}+\cos ^{-1} x\right)=\cos \left(\frac{\pi}{2}\right)$
$\Rightarrow \sin ^{-1} \frac{2}{5}+\cos ^{-1} x=\frac{\pi}{2}$
$\therefore x=\frac{2}{5} \quad\left[\because \sin ^{-1} y+\cos ^{-1} y=\frac{\pi}{2}\right]$
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