Question

cos72°—cos36°=____

Answer 1

解答：
不知你有没有学过和差化积公式，
以下按没学过处理（如果学过，可以简化以下步骤）
cos72°—cos36°
=cos(54°+18°)-cos(54°-18°)
=cos54°cos18°-sin54°sin18°-(cos54°cos18°+sin54°sin18°)
=-2sin54°sin18°
=-2cos36°cos72°
=-2sin36°cos36°cos72°/(sin36°)
=-sin72°cos72°/(sin36°)
=-2sin72°cos72°/(2sin36°)
=-sin144°/(2sin36°)
∵ sin144°=sin(180°-36°)=sin36°
∴ 原式=-1/2
即 cos72°—cos36°=-1/2

Answer 2

cos72°-cos36°
=cos(54+18)-cos(54-18)
=[cos54cos18-sin54sin18]-[cos54cos18+sin54sin18]
=-2sin54sin18 (sin54=cos36)
=-2cos36sin18
=-2cos36sin18cos18/cos18
=-cos36sin36/cos18
=-sin72/(2cos18)
=-sin72/(2sin72)
=-1/2