3sinB-sin(2X+B)=0,则tan(X+B)-2tanX=
问题描述：
3sinB-sin(2X+B)=0,则tan(X+B)-2tanX=
答
3sinB-sin(2x+B)=0
3sin(x+B-x)-sin(x+B+x))=0
3sin(x+B)cosx-3cos(x+B)sinx=sin(x+B)cosx+cos(x+B)sinx
（两边同时除cos(x+B)cosx)
3tan(x+B)-3tanx=tan(x+B)+tanx
tan(x+B)=2tanx
所以
tan(X+B)-2tanX=0
答
sinB=sin(X+B-X)=sin(X+B)cosX-cos(X+B)sinXsin(2X+B)=sin(X+B+X)=sin(X+B)cosX+cos(X+B)sinX代入3sinB-sin(2X+B)=0得 2sin(X+B)cosX-4cos(X+B)sinX=02tan(X+B)-4tanX=0tan(X+B)-2tanX=0