Answer
$-1$
Work Step by Step
1. Let $sin^{-1}(-\frac{4}{5})=u$ (quadrant IV), we have $sin(u)=-\frac{4}{5}, cos(u)=\frac{3}{5}$
2. Let $tan^{-1}(\frac{3}{4})=v$ (quadrant I), we have $tan(v)=\frac{3}{4}, sin(v)=\frac{3}{5},cos(v)=\frac{4}{5}$
3. $sin(u-v)=sin(u)cos(v)-cos(u)sin(v)=(-\frac{4}{5})(\frac{4}{5})-(\frac{3}{5})(\frac{3}{5})=-1$
