Question 1014959
sec a = -5/3 ==> 1 + tan^2 a = 25/9 ==> tan^2 a = 16/9 ==>tan a = -4/3 (Angle a is in the 2nd quadrant because 90° < a < 180°.)

sin b = 5/13 ==> 1+ cot^2 b = 169/25 ==> cot^2 b = 144/25 ==> cot b = -12/5 (Angle b also in the 2nd quadrant because 90° < b < 180°.)

==> tan b = -5/12.

==> {{{tan(a+b) = (tan a + tan b)/(1-tan a*tan b)=(-4/3 - 5/12)/(1-(-4/3)*(-5/12))=-63/16}}}