原式
=（cosα+cos(120°-α))²-cosαcos(120°-α)
=(2cos60°cos(α-60°))²-(cos120°+cos(2α-120°))/2 ----利用和差化积、积化和差公式,可以百科搜
=cos²(α-60°)-(cos(2α-120°))/2+1/4
=(1+cos(2α-120°))/2-cos(2α-120°))/2+1/4
=3/4