化简 sin^2(派/3+α)+sin^(派/6-α)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/14 14:30:17
化简 sin^2(派/3+α)+sin^(派/6-α)
根据cos2x=1-2sin²x
得sin²x=(1-cos2x)/2
sin²(π/3+α)+sin²(π/6-α)
=[1-cos2(π/3+α)]/2+[1-cos2(π/6-α)]/2
=[2-cos(2π/3+2α)-cos(π/3-2α)]/2
=[2-cos(2π/3)cos2α+sin(2π/3)sin2α-cos(π/3)cos2α-sin(π/3)sin2α]/2
=[2+cos2α/2+(√3/2)*sin2α-cos2α/2-(√3/2)*sin2α]/2
=2/2
=1
得sin²x=(1-cos2x)/2
sin²(π/3+α)+sin²(π/6-α)
=[1-cos2(π/3+α)]/2+[1-cos2(π/6-α)]/2
=[2-cos(2π/3+2α)-cos(π/3-2α)]/2
=[2-cos(2π/3)cos2α+sin(2π/3)sin2α-cos(π/3)cos2α-sin(π/3)sin2α]/2
=[2+cos2α/2+(√3/2)*sin2α-cos2α/2-(√3/2)*sin2α]/2
=2/2
=1
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