Answer
$\frac{9}{10}$
Work Step by Step
1. Let $sin^{-1}(\frac{3}{5})=t$, we have $sin(t)=\frac{3}{5}$ and $cos(t)=\frac{4}{5}$
2. $cos^2(\frac{1}{2}sin^{-1}(\frac{3}{5}))=cos^2(\frac{1}{2}t)=\frac{1+cos(t)}{2}=\frac{1+\frac{4}{5}}{2}=\frac{9}{10}$
