原式=cos²x+{-cos[180-(x+120)]}²+{-cos[180-(x+240)]}²
=cos²x+cos²(60-x)+cos²(60+x)
=cos²x+(cos60cosx+sin60sinx)²+(cos60cosx-sin60sinx)²
=cos²x+(1/2cosx+√3/2sinx)²+(1/2cosx-√3/2sinx)²
=cos²x+1/4cos²x+√3/2sinxcosx+3/4sin²x+1/4cos²x-√3/2sinxcosx+3/4sin²x
=3/2*cos²x+3/2sin²x
=3/2(sin²x+cos²x)
=3/2