Answer
$-\frac{24}{25}$
Work Step by Step
Step 1. Letting $sin^{-1}(\frac{3}{5})=u$, we have $sin(u)=\frac{3}{5}$, thus $cos(u)=\frac{4}{5}$
Step 2. Letting $cos^{-1}(-\frac{4}{5})=v$, we have $cos(v)=-\frac{4}{5}$, thus $sin(v)=\frac{3}{5}$
Step 3. $sin(u-v)=sin(u)cos(v)-cos(u)sin(v)=(\frac{3}{5})(-\frac{4}{5})-(\frac{4}{5})(\frac{3}{5})=-\frac{12+12}{25}=-\frac{24}{25}$
