Question

if sin x = 3/5 and sin y = 5/13 what is the value of cos (x-y)

Answer 1

recalling your basic 3-4-5 and 5-12-13 right triangles, you know that

cosx = 4/5
cosy = 12/13
Now just do
cos(x-y) = cosx cosy + sinx siny