Question

If $\begin{array}{c}\sin ({\sin }^{-1}\frac{1}{5}+{\cos }^{-1}x)=1\end{array}$, then $x$ is equal to

• A. $1$
• B. $0$
• C. $\begin{array}{c}\frac{4}{5}\end{array}$
• D. $\begin{array}{c}\frac{1}{5}\end{array}$

Answer 1

The correct option is D $\begin{array}{c}\frac{1}{5}\end{array}$

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