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)

tan(A+B)=2tanAsin(A+B)/cos(A+B)=2sinA/cosAsin(A+B)*cosA=2sinA*cos(A+B) sin(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)3sinB=sin(2A+B)