若tan(A+B)=2tanA,求证3sinB=sin(2A+B)
问题描述:
若tan(A+B)=2tanA,求证3sinB=sin(2A+B)
答
tan(A+B)=2tanAsin(A+B)*cosA=2sinA*cos(A+B) ①sin(A+B)*cosA-sinA*cos(A+B)=sinA*cos(A+B)sinB=sinA*cos(A+B)sin(2A+B)=sin(A+B)*cosA+sinA*cos(A+B)=3sinA*cos(A+B)(因为①)3sinB=sin(2A+B)