Question

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

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

Answer 1

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

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

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

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