Express sin(x+2y)-sin(x-2y) in terms of cosx only where y is acute
From your sum-to-product formulas,
sinA-sinB = 2 cos(A+B)/2 sin(A-B)/2
Using your values, that would be
2 cosx sin2y
without knowing more about the relation between x and y, that's as far as we can go.
If you supply the missing info, I'm sure you can finish it off.