If $\cos A=\frac{5}{13},\tan B=\frac{-15}{8},270°<A<360°,90°<B<180°,$ then the quadrant to which A+B belongs is

cosA=5/13 andsinA=-12/13

tanB=-15/8 and sinB=15/17;cosB=-8/17

$\sin (A+B)=\left(\frac{{\displaystyle -12}}{{\displaystyle 13}}\right)\left(\frac{{\displaystyle -8}}{{\displaystyle 17}}\right)+\frac{5}{13}\frac{15}{17}=\frac{96+75}{221}>0$

$\cos (A+B)=\frac{5}{13}\left(\frac{{\displaystyle -8}}{{\displaystyle 17}}\right)-\left(\frac{{\displaystyle -12}}{{\displaystyle 13}}\right)\left(\frac{{\displaystyle 15}}{{\displaystyle 17}}\right)=\frac{-40+180}{221}>0$

$\therefore A+B\in Q_1(\because 360°<A+B<540°)$ 

sin(A+B) and cos(A+B) both positive implies lies in first quadrant