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