Question

If $\sin ({\sin }^{-1}\frac{4}{5}+{\cos }^{-1}x)=1$, then find the value of $x$.

• A. $\frac{2}{5}$
• B. $\frac{3}{5}$
• C. $\frac{1}{5}$
• D. $\frac{4}{5}$

Answer 1

The correct option is D $\frac{4}{5}$

Consider the given equation.

$\sin ({\sin }^{-1}\frac{4}{5}+{\cos }^{-1}x)=1$

${\sin }^{-1}\frac{4}{5}+{\cos }^{-1}x={\sin }^{-1}1$

${\sin }^{-1}\frac{4}{5}+{\cos }^{-1}x=\frac{\pi }{2}$

${\sin }^{-1}\frac{4}{5}=\frac{\pi }{2}-{\cos }^{-1}x$

${\sin }^{-1}\frac{4}{5}={\sin }^{-1}x\therefore ({\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2})$

$x=\frac{4}{5}$

Hence, this is the answer.