3sinB-sin(2X+B)=0,则tan(X+B)-2tanX=

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 14:33:03
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=

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