计算cos²θ+cos²(θ+2π/3)+cos²(θ-2π/3)

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计算cos²θ+cos²(θ+2π/3)+cos²(θ-2π/3)
计算cos²θ+cos²(θ+2π/3)+cos²(θ-2π/3)

计算cos²θ+cos²(θ+2π/3)+cos²(θ-2π/3)
原式=cos²θ+(cosθcos2π/3-sinθsin2π/3)²+(cosθcos2π/3+sinθsin2π/3)²
=cos²θ+(-1/2*cosθ-√3/2*sinθ)²+(-1/2*cosθ+√3/2*sinθ)²
=cos²θ+1/4*cos²θ+√3/2*sinθcosθ+3/4*sin²θ+1/4*cos²θ-√3/2*sinθcosθ+3/4*sin²θ
=3/2*cos²θ+3/2*sin²θ
=3/2*(cos²θ+sin²θ)
=3/2