化简cos24°cos36°-cos66°cos54°cos58°sin37°+sin122°sin53°cos(π/3
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/02 20:16:10
化简
cos24°cos36°-cos66°cos54°
cos58°sin37°+sin122°sin53°
cos(π/3+θ)+cos(π/3-θ)
cos(α-β)cos(α+β)+sin(α-β)sin(α+β)
cos24°cos36°-cos66°cos54°
cos58°sin37°+sin122°sin53°
cos(π/3+θ)+cos(π/3-θ)
cos(α-β)cos(α+β)+sin(α-β)sin(α+β)
cos24°cos36°-cos66°cos54°=cos24°cos36°-sin24sin36=cos(24+36)=cos60=1/2
cos58°sin37°+sin122°sin53°=cos58°sin37°+sin58°cos37=sin(58+37)=1
cos(π/3+θ)+cos(π/3-θ)=2*cos[(π/3+θ)+(π/3-θ)]/2*cos[(π/3+θ)-(π/3-θ)]/2=cosθ
cos(α-β)cos(α+β)+sin(α-β)sin(α+β)=cos[(α-β)-(α+β)]=cos2β
cos58°sin37°+sin122°sin53°=cos58°sin37°+sin58°cos37=sin(58+37)=1
cos(π/3+θ)+cos(π/3-θ)=2*cos[(π/3+θ)+(π/3-θ)]/2*cos[(π/3+θ)-(π/3-θ)]/2=cosθ
cos(α-β)cos(α+β)+sin(α-β)sin(α+β)=cos[(α-β)-(α+β)]=cos2β
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