已知cos (π/6 -α)=√3/3 ,求cos (5π/6 + α)-sin²(α -π/6)的值

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已知cos (π/6 -α)=√3/3 ,求cos (5π/6 + α)-sin²(α -π/6)的值

已知cos (π/6 -α)=√3/3 ,求cos (5π/6 + α)-sin²(α -π/6)的值
已知cos (π/6 -α)=√3/3 ,求cos (5π/6 + α)-sin²(α -π/6)的值

已知cos (π/6 -α)=√3/3 ,求cos (5π/6 + α)-sin²(α -π/6)的值
cos (5π/6 + α)-sin²(α -π/6)
=cos(π-(π/6-α))-1+cos²(α-π/6)
=-cos(π/6-α)-1+cos²(π/6-α)
=-√3/3-1+(√3/3)² 其中cos (π/6 -α)=√3/3
=-√3/3-1+1/3
=-(2+√3)/3