cosX+cos(X+120°)+cos(X+240°)请问答案怎么求出为0 ,

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cosX+cos(X+120°)+cos(X+240°)请问答案怎么求出为0 ,

cosX+cos(X+120°)+cos(X+240°)请问答案怎么求出为0 ,
cosX+cos(X+120°)+cos(X+240°)请问答案怎么求出为0 ,

cosX+cos(X+120°)+cos(X+240°)请问答案怎么求出为0 ,
cos(X+120°)=cosxcos120°-sinxsin120°
cos(X+240°)=cos(x-120°)=cosxcos120°+sinxsin120°
cos(X+120°)+cos(X+240°)=2*cosxcos120°=2cosx*(-1/2)=-cosx
原式=cosx-cosx=0

原式=cosx+cosxcos120-sinxsin120+cosxcos240-sinxsin240
=cosx+cosx*(-1/2)-sinx*(√3/2)+cosx*(-1/2)-sinx*(-√3/2)
=0

cosx+cos (x+120)+cos (x+240)=cox+cos x*cos120-sinx *sin120+cos x*cos240-sinx*sin240=cosx+cosx*(-cos60)-sinx*sin60+cosx*(-cos60)-sinx*(-sin60)=cosx-2cosx*cos60=cosx-cosx=0 数字单位均为度