cosθ^2+cos(θ+2π/3)^2+cos(θ-2π/3)^2 计算
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/02 19:27:10
cosθ^2+cos(θ+2π/3)^2+cos(θ-2π/3)^2 计算
cos^2θ+cos^2(θ+2π/3)+cos^2(θ-2π/3)
=(1+cos2θ)/2+[1+cos(2θ+4π/3)]/2+[1+cos(2θ-4π/3)]/2
=3/2 +[cos2θ+cos(2θ+4π/3)+cos(2θ-4π/3)]/2
cos2θ+cos(2θ+4π/3)+cos(2θ-4π/3)
=cos2θ+cos2θcos(4π/3)-sin2θsin(4π/3)+cos2θcos(4π/3)+sin2θsin(4π/3)
=cos2θ+2cos2θcos(4π/3)
=0
所以 原式=3/2
=(1+cos2θ)/2+[1+cos(2θ+4π/3)]/2+[1+cos(2θ-4π/3)]/2
=3/2 +[cos2θ+cos(2θ+4π/3)+cos(2θ-4π/3)]/2
cos2θ+cos(2θ+4π/3)+cos(2θ-4π/3)
=cos2θ+cos2θcos(4π/3)-sin2θsin(4π/3)+cos2θcos(4π/3)+sin2θsin(4π/3)
=cos2θ+2cos2θcos(4π/3)
=0
所以 原式=3/2
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