Sin and cos property

It is based on the following result :
sin (x + y) - sin ( x - y) = sin x cos y + cos x sin y - ( sin x cos y - sin y cos x)
= 2 cos x sin y.
Now x + y = 3π/8....(1)
x - y = π/8 ............(2)
(1) + (2) we get 2x = 3π/8 + π/8 = 4π/8, so x = 2π/8 = π/4.
so y = 3π/8 - x = 3π/8 - π/4 = π/8
Therefore, the answer is 2 cos π/4 sin π/8.

2011-12-03 07:48:10 補充：
Correction : I missed out the n, so please add back the n. That is x + y = 3πn/8 and x - y = πn/8.