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