Answer
$y\sqrt {1-x^2}-x\sqrt {1-y^2}$
Work Step by Step
Step 1. Let $u=sin^{-1}x, v=cos^{-1}y$, we have $sin(u)=x, cos(v)=y$ and $cos(u)=\sqrt {1-x^2}, sin(v)=\sqrt {1-y^2}$ (Pythagorean Identities)
Step 2. Use the Addition Formula, $cos(sin^{-1}x+cos^{-1}y)=cos(u+v)=cos(u)cos(v)-sin(u)sin(v)
=y\sqrt {1-x^2}-x\sqrt {1-y^2}$
