3sinB-sin(2X+B)=0,则tan(X+B)-2tanX=

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3sinB-sin(2X+B)=0,则tan(X+B)-2tanX=3sinB-sin(2X+B)=0,则tan(X+B)-2tanX=3sinB-sin(2X+B)=0,则tan(X+B)-2tan

3sinB-sin(2X+B)=0,则tan(X+B)-2tanX=
3sinB-sin(2X+B)=0,则tan(X+B)-2tanX=

3sinB-sin(2X+B)=0,则tan(X+B)-2tanX=
sinB=sin(X+B-X)=sin(X+B)cosX-cos(X+B)sinX
sin(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=0
2tan(X+B)-4tanX=0
tan(X+B)-2tanX=0

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