So the problem is asking to find cos(α+β)

Question

The problem gives me
sinα= 12/13, 0<α<π/2
cosβ= 21/29, 0<β<π/2

The answer is -135/377

I have no idea how to start solving to find that answer.

Answer 1

For each of the given trig ratios, make a sketch of the corresponding right-angled triangles

sinα = 12/13 , so y = 12, r = 13
x^2 + y^2 = r^2
x^2 + 144 = 169
x^2 = 25
x = 5 in quad I , so
sinα = 12/13 , cosα = 5/13

cosβ = 21/29 in quadrant I
x = 21, r=29
y = 20
sinβ = 20/29 , cosβ = 21/29

You should have learned that
cos(α+β) = cosαcosβ - sinαsinβ
= (5/13)(21/29)- (12/13)(20/29)
= -135/377

Answer 2

Thank you ^^