化简:(cosA)^2+[cos(2/3pai+A)]^2+[cos(2/3pai-A)]^2

问题描述:

化简:(cosA)^2+[cos(2/3pai+A)]^2+[cos(2/3pai-A)]^2

(cosA)^2+[cos(2π/3+A)]^2+[cos(2π/3-A)]^2=(cosA)^2+[1+cos(4π/3+2A)]/2+[1+cos(4π/3-2A)]/2=(cosA)^2+1/2+1/2*cos(4π/3+2A)+1/2+1/2*cos(4π/3-2A)=(cosA)^2+1/2*cos(4π/3+2A)+1/2*cos(4π/3-2A)+1=(cosA)^2...