cos144°=cos(90°+54°）=-sin54°
则
cos24°cos54°－sin24°cos144°=cos24°cos54°+sin24°sin54°
由cosacosb+sinasinb=cos(a-b)得
原式=cos(54°-24°)
=cos30°
=√3/2
cos144°=cos(90°+54°）=-sin54°
则
cos24°cos54°－sin24°cos144°=cos24°cos54°+sin24°sin54°
由cosacosb+sinasinb=cos(a-b)得
原式=cos(54°-24°)
=cos30°
=√3/2