tan A=-4/5;A in Quadrant 2 and cos B=-5/13: B in Quadrant 3.

Question

What is the exact value of the expression cos(A+B)?

Answer 1

draw your triangles in standard position. It will be clear that

sinA = 4/√41
cosA = -5/√41

sinB = -12/13
cosB = -5/13

Now just plug that into the formula for cos(A+B)

Although I suspect a typo...

Answer 2

73*41^1/2/533