Question

If
$\sin \left({\sin }^{-1}\left(\frac{3}{5}\right)+{\cos }^{-1}x\right)=1,$
then find the value of x.

• A. $\frac{4}{5}$
• B. $0$
• C. $\frac{3}{5}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is C $\frac{3}{5}$

$\sin \left({\sin }^{-1}\left(\frac{3}{5}\right)+{\cos }^{-1}x\right)=1$
$\Rightarrow {\sin }^{-1}\left(\frac{3}{5}\right)+{\cos }^{-1}x={\sin }^{-1}1$
$\Rightarrow {\sin }^{-1}\left(\frac{3}{5}\right)=\frac{\pi }{2}-{\cos }^{-1}x$
$\Rightarrow {\sin }^{-1}\left(\frac{3}{5}\right)={\sin }^{-1}x$
$\therefore x=\frac{3}{5}$