Question

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

• A. $\frac{1}{5}$
• B. $\frac{4}{5}$
• C. $0$
• D. $1$

Answer 1

The correct option is A $\frac{1}{5}$

$\sin ({\sin }^{-1}\frac{1}{5}+{\cos }^{-1}x)=1\Rightarrow {\sin }^{-1}\frac{1}{5}+{\cos }^{-1}x=\frac{\pi }{2}\Rightarrow {\sin }^{-1}\frac{1}{5}=\frac{\pi }{2}-{\cos }^{-1}x={\sin }^{-1}x\therefore x=\frac{1}{5}$
$(\because {\cos }^{-1}x+{\sin }^{-1}x=\frac{\pi }{2};x\in [-1,1\left]\right)$