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)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 20:51:02

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)
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)

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°=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

=1/2