Question

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

Answer 1

$\begin{array}{c}\sin \left({\sin }^{-1}\frac{1}{5}\right)+{\cos }^{-1}x=1\\ \Rightarrow \frac{1}{5}+{\cos }^{-1}x=1\\ \Rightarrow {\cos }^{-1}x=1-\frac{1}{5}\\ \Rightarrow {\cos }^{-1}x=\frac{4}{5}\\ x=\cos \frac{4}{5}\end{array}$