已知tan=2,求cos^4(π/3+α)-cos^4(α-π/6)的值

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已知tan=2,求cos^4(π/3+α)-cos^4(α-π/6)的值

已知tan=2,求cos^4(π/3+α)-cos^4(α-π/6)的值
已知tan=2,求cos^4(π/3+α)-cos^4(α-π/6)的值

已知tan=2,求cos^4(π/3+α)-cos^4(α-π/6)的值
tanα=2,根据万能公式,得cos2α=-3/5,sin2α=4/5;
原式=cos^4(π/3+α)-cos^4(π/6-α)=cos^4(π/3+α)-sin^4(π/3+α)
=cos^2(π/3+α)-sin^2(π/3+α)=cos(2π/3+2α)= -(cos2α)/2+根号3*sin2α/2=(3+4*根号3)/10.