Angle a lies in the second quadran and angle b lies in the third quadrant such that cos a = -3/5 and tan b = 24/7. Determine an exact value for cos (a+b), sin(a-b)

Answer 1

sin a = 4/5
sin b = -24/25
cos b = -7/25

cos(a+b) = cosa*cosb-sina*sinb
= (-3/5)(-7/25) - (4/5)(-24/25)
= 21/125 + 96/125
= 117/125

now apply the formula for sin(a-b) the same way.