Answer
See below.
Work Step by Step
1. Let $sin^{-1}v=x$, we have $sin(x)=v, cos(x)=\sqrt {1-v^2}$
2. Let $cos^{-1}v=y$, we have $cos(y)=v, sin(y)=\sqrt {1-v^2}$
3. $cos(x+y)=cos(x)cos(y)-sin(x)sin(y)=(\sqrt {1-v^2})(v)-(v)(\sqrt {1-v^2})=0$
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