sinx+siny
=sin[(x+y)/2+(x-y)/2]+sin[(x+y)/2-(x-y)/2]
=sin(x+y)/2 cos(x-y)/2 + sin(x-y)/2 cos(x+y)/2
+sin(x+y)/2 cos(x-y)/2 - sin(x-y)/2 cos(x+y)/2
=2sin(x+y)/2 cos(x-y)/2