化简sinθ+cos(θ+2π/3)+cos(θ+4π/3)
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化简sinθ+cos(θ+2π/3)+cos(θ+4π/3)
化简sinθ+cos(θ+2π/3)+cos(θ+4π/3)
化简sinθ+cos(θ+2π/3)+cos(θ+4π/3)
原式=sinθ-(1/2)cosθ-(√3/2)sinθ-(1/2)cosθ+(√3/2)sinθ
=sinθ-cosθ
=√2sin(θ-π/4)
sinθ+cos(θ+2π/3)+cos(θ+4π/3)=sinθ+cosθcos2π/3-sinθsin2π/3+cosθcos4π/3-sinθsin4π/3
=sinθ-1/2cosθ-√3/2sinθ-1/2cosθ+√3/2sinθ
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sinθ+cos(θ+2π/3)+cos(θ+4π/3)=sinθ+cosθcos2π/3-sinθsin2π/3+cosθcos4π/3-sinθsin4π/3
=sinθ-1/2cosθ-√3/2sinθ-1/2cosθ+√3/2sinθ
=sinθ-cosθ
=√2sin(θ-π/4)
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