Use the given information to evaluate cos (a+b). Sin a = -7/25, cot b = -8/15. Neither a nor b are in quadrant IV. exact answers only. No decimals.

Answer 1

since the sine is negative in III or IV and the cotangent is negative in II or IV, and we are told that neither is in IV
a must be in III and b must be in II

sin a = -7/25, a in III
cos a = -24/25

cot b = -8/15 , b in II
tan b = -15/8
sinb = 15/17
cosb = -8/17

cos(a+b)
= cosa cosb - sina sinb
= (-24/25)(-8/17) - (-7/25)(15/17)
= 297/425