Question

Find the value of $\cos \left({\cos }^{-1}x+{\sin }^{-1}x\right)at,x=\frac{1}{5}$

Answer 1

Consider the given expression,

$\Rightarrow \cos ({\cos }^{-1}x+{\sin }^{-}x)$

Put, $x=\frac{1}{5}$, we get

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

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

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

Hence, this is the answer.