Question

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

Answer 1

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

$\Rightarrow {\sin }^{-1}\frac{2}{5}+{\cos }^{-1}x={\cos }^{-1}0$

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

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

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

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

$\Rightarrow x=\frac{2}{5}$