cosx+cos(120°-x)+cos(120°+x)

来源:学生作业帮助网 编辑:六六作业网 时间:2025/01/23 07:01:35
cosx+cos(120°-x)+cos(120°+x)cosx+cos(120°-x)+cos(120°+x)cosx+cos(120°-x)+cos(120°+x)cos(120°+x)=cos1

cosx+cos(120°-x)+cos(120°+x)
cosx+cos(120°-x)+cos(120°+x)

cosx+cos(120°-x)+cos(120°+x)
cos(120°+x)
=cos120°cosx-sin120°sinx
=-cos60°cosx-sin60°sinx
=-1/2 cosx-√3/2 sinx
同理,
cos(120°-x)=-1/2 cosx+√3/2 sinx
所以原式
=cosx-1/2 cosx-1/2 cosx
=0