If $ \arcsin x+ \arcsin y=\frac{\pi}{2}$, prove that $ x^2+y^2=1$. If $ \arcsin x+ \arcsin y=\frac{\pi}{2}$,
prove that $$ x^2+y^2=1$$
I tried taking sine of both the sides, I only come to this result: $$x^2 + y^2 -2x^2y^2 + 2xy\sqrt{(1-y^2)(1+x^2)}=1.$$

As $\arccos  u+\arcsin u=\dfrac\pi2 $
from the given relation, $\arccos x+\arccos y=\dfrac\pi2$
Taking cosine in both sides, $$xy-\sqrt{(1-x^2)(1-y^2)}=0\iff xy=\sqrt{(1-x^2)(1-y^2)}$$
Now square both sides.
