sin(A+B)-sinA=2cos(A+B/2)*sinB/2怎么推导?

sin(A+B)-sinA=2cos(A+B/2)*sinB/2怎么推导?
sin(A+B)-sinA=2cos(A+B/2)*sinB/2怎么推导?

sin(A+B)-sinA=2cos(A+B/2)*sinB/2怎么推导?
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.

sin(A+B)-sin(A)=sin[(A+B/2)+B/2]-sin[(A+B/2)-B/2]
展开即可
此公式为和差化积公式其一