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)

Question

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)

Answer 1

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