Answer
See below.
Work Step by Step
Step 1. Letting $sin^{-1}v=x$, we have $sin(x)=v$ and $cos(x)=\sqrt {1-v^2}$
Step 2. Letting $cos^{-1}v=y$, we have $cos(y)=v$ and $sin(y)=\sqrt {1-v^2}$
Step 3. We have $sin(x+y)=sin(x)cos(y)+cos(x)sin(y)=(v)(v)+(\sqrt {1-v^2})(\sqrt {1-v^2})=1$
