cosa^2+cos(2π/3-a)^2+cosacos（2π/3-a）化简

题目

cosa^2+cos(2π/3-a)^2+cosacos（2π/3-a）化简
Rt,谢谢

答案

cos²a+cos²(2π/3-a)+cosacos（2π/3-a）
=[cosa+cos(2π/3-a)]²-cosacos（2π/3-a）
=[2cosπ/3cos(a-π/3)]²-1/2[cos2π/3+cos(2a-2π/3）]
=cos²(a-π/3)+1/4-1/2cos(2a-2π/3）
=cos²(a-π/3)+1/4-1/2[2cos²(a-π/3）-1]
=cos²(a-π/3)+1/4-cos²(a-π/3）+1/2
=3/4