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

sin(A+B)-sinA=2cos(A+B/2)*sinB/2怎么推导?

人气：345 ℃　时间：2020-04-06 06:37:08

解答

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.