Sum and difference identities

Question

Use the information given below to find tan+αβ

tan a=5/12, with a in quadrant I

cos b=8/17, with b in quadrant IV

give exact answer not a decimal approximation

tan(a+b)=

Please help and explain

Answer 1

Since cos(b) = 8/17 and angle b lies in quadrant 4, sin(b) = -√[1 - cos²(b)] = -15/17

So, tan(b) = sin(b) / cos(b) = -15/8

tan(a + B) = [tan(a) + tan(b)] / [1 - tan(a)tan(b)]

= [5/12 - 15/8] / [1 + 75/96] = (-140/96) / (171/96) = -140 / 171