Answer
$\frac{4+3\sqrt 3}{10}$
Work Step by Step
Step 1. Letting $sin^{-1}\frac{3}{5}=x$, we have $sin(x)=\frac{3}{5}$ and $cos(x)=\frac{4}{5}$
Step 2. Letting $cos^{-1}\frac{1}{2}=y$, we have $cos(y)=\frac{1}{2}$ and $sin(y)=\frac{\sqrt 3}{2}$
Step 3. We have $cos(x-y)=cos(x)cos(y)+sin(x)sin(y)=(\frac{4}{5})(\frac{1}{2})+(\frac{3}{5})(\frac{\sqrt 3}{2})=\frac{4+3\sqrt 3}{10}$
