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