Answer
$\frac{\sqrt 3}{2}$
Work Step by Step
1. Let $sin^{-1}\frac{\sqrt 3}{2}=t$, we have $sin(t)=\frac{\sqrt 3}{2}$ and $cos(t)=\frac{1}{2}$
2. $sin(2sin^{-1}\frac{\sqrt 3}{2})=sin(2t)=2sin(t)cos(t)=2(\frac{\sqrt 3}{2})(\frac{1}{2})=\frac{\sqrt 3}{2}$