Question

If $({\sin }^{-1}x{)}^2+({\sin }^{-1}y{)}^2+2\left({\sin }^{-1}x\right)\left({\sin }^{-1}y\right)={\pi }^2$, then $x^2+y^2$ is equal to -

• A. 1
• B. 3/2
• C. 2
• D. 1/2

Answer 1

The correct option is C 2

$({\sin }^{-1}x+{\sin }^{-1}y{)}^2={\pi }^2$
$\Rightarrow {\sin }^{-1}x+{\sin }^{-1}y=\pm \pi$
$\Rightarrow {\sin }^{-1}x={\sin }^{-1}y=\frac{\pi }{2}$
or ${\sin }^{-1}x={\sin }^{-1}y=-\frac{\pi }{2}$
$\Rightarrow x^2+y^2=2$