Question

最后得出结果的地方，看不懂了，三角函数是怎么直接变成数值了？高中数学

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Answer 1

拆开之后消掉了2θ

Answer 2

解答的第三步错了，cos(2θ+8π/3)≠cos(2θ-π/3)，
而应该是cos(2θ+8π/3)=cos(2θ+3π-π/3)=-cos(2θ-π/3)
所以分子1+cos2θ+1+cos(2θ+4π/3)+1+cos(2θ+8π/3)
=3+cos2θ-cos(2θ+π/3)-cos(2θ-π/3)
=3+cos2θ-[(1/2)cos2θ-(√3/2)sin2θ]-[(1/2)cos2θ+(√3/2)sin2θ]
=3+cos2θ-(1/2)cos2θ+(√3/2)sin2θ-(1/2)cos2θ-(√3/2)sin2θ
=3
1-cos2θ+1-cos(2θ+4π/3)+1-cos(2θ+8π/3)
=3-cos2θ+cos(2θ+π/3)+cos(2θ-π/3)
=3-cos2θ+(1/2)cos2θ-(√3/2)sin2θ+(1/2)cos2θ+(√3/2)sin2θ
=3

Answer 3

因为消掉了
从倒数第三部直接和差化积就可以了，
变形显得多余