sin(A+B)-sinA=sin [(A+B/2)+ B/2]-sin[(A+B/2)- B/2]
=[sin(A+B/2)cos B/2+cos(A+B/2)sin B/2]
-[ sin(A+B/2)cos B/2-cos(A+B/2)sin B/2]
=2 cos(A+B/2)sin B/2.
∴原式成立.