# if

Question:

If $\cos \left(\sin ^{-1} \frac{2}{5}+\cos ^{-1} x\right)=0$, find the value of $x$

Solution:

$\cos \left(\sin ^{-1} \frac{2}{5}+\cos ^{-1} x\right)=0$

$\Rightarrow \cos \left(\sin ^{-1} \frac{2}{5}+\cos ^{-1} x\right)=\cos \left(\frac{\pi}{2}\right)$

$\Rightarrow \sin ^{-1} \frac{2}{5}+\cos ^{-1} x=\frac{\pi}{2}$

$\therefore x=\frac{2}{5} \quad\left[\because \sin ^{-1} y+\cos ^{-1} y=\frac{\pi}{2}\right]$