Taking Rhs
1/2 [sin(x+y)+ sin (x-y)]
using sinA + sin B = 2 cos (A+B)/2 cos( A - B)/2
1/2 [ 2 Cos ( x+y+x-y)/2 . Cos (x+y-x+y)/2]
=Cos 2x/2. Cos 2y/2 = Cos x . Cos y
Hence true
