Question

If $\cos ({\sin }^{-1}\frac{2}{5}+{\cos }^{-1}x)=0$, find the value of x.

• A. $\frac{3}{7}$
• B. $\frac{1}{5}$
• C. $\frac{2}{5}$
• D. $\frac{4}{9}$

Answer 1

The correct option is C $\frac{2}{5}$

$\cos ({\sin }^{-1}\frac{2}{5}+{\cos }^{-1}x)=0$

${\sin }^{-1}\frac{2}{5}+{\cos }^{-1}x={\cos }^{-1}0$

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

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

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

$x=\frac{2}{5}$