Question

怎么证明sinA+sinB-sinC=4sin(A/2)sin(B/2)cos(C/2)

要过程,谢谢

Answer 1

A,B,C是三角形的三个角吧！右边=4sinA/2sinB/2sin（A+B）/2 =4sinA/2sinB/2[sinA/2cosB/2+sinB/2cosA/2] =4(sinA/2)sinB/2cosB/2+4(sinB/2）sinA/2cosA/2 =2(sinA/2)sinB+2(sinB/2)sinA =sinB(1-sinA)+sinA(1-sinB) =sinA+sinB-sinAcosB-sinBcosA =sinA+sinB-sin(A+B) =sinA+sinB-sinC =左边