Answer
$\frac{1}{5}$
Work Step by Step
1. Let $cos^{-1}(\frac{3}{5})=t$, we have $cos(t)=\frac{3}{5}$
2. $sin^2(\frac{1}{2}cos^{-1}(\frac{3}{5}))=sin^2(\frac{1}{2}t)=\frac{1-cos(t)}{2}=\frac{1-\frac{3}{5}}{2}=\frac{1}{5}$
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