Answer
$tan(u+v)=\frac{24}{7}$
Work Step by Step
$cos^2v+sin^2v=1$
$\frac{16}{25}+sin^2v=1$
$sin^2v=\frac{9}{25}$
$sin~v=±\frac{3}{5}~~$ (But, $v$ is in Quadrant III):
$sin~v=-\frac{3}{5}$
$tan~v=\frac{sin~v}{cos~v}=\frac{-\frac{3}{5}}{-\frac{4}{5}}=\frac{3}{5}·\frac{5}{4}=\frac{3}{4}$
$tan(u+v)=\frac{tan~u+tan~v}{1-tan~u~tan~v}=\frac{\frac{3}{4}+\frac{3}{4}}{1-\frac{3}{4}·\frac{3}{4}}=\frac{\frac{3}{2}}{1-\frac{9}{16}}=\frac{\frac{3}{2}}{\frac{7}{16}}=\frac{3}{2}·\frac{16}{7}=\frac{24}{7}$
