cosα+cos(120°-α）+cos(120+α)
=cosα+(cos120cosα+sin120sinα)+(cos120cosα-sin120sinα)
=cosα+cos120cosα+sin120sinα+cos120cosα-sin120sinα
=cosα+2*cos120cosα
=cosα+2*cos(90+30)cosα
=cosα+2*(-1/2)cosα
=cosα+(-cosα)
=0