Answer
$\frac{3}{5}$
Work Step by Step
Step 1. Let $u=tan^{-1}(-\frac{4}{3})$. We have $tan(u)=-\frac{4}{3}$ and $-\frac{\pi}{2}\lt u\leq 0$
Step 2. Form a right triangle with angle $u$ and sides $4,3,5$, we have $cos(u)=\frac{3}{5}$
Step 3. We have $cos[tan^{-1}(-\frac{4}{3})]=cos(u)=\frac{3}{5}$
