Question

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

• A. 1
• B. $3/2$
• C. 2
• D. $1/2$

Answer 1

Answer: (C)

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