cos36°-cos72°=？具体过程

来源：百度知道 编辑：UC知道 时间：2024/04/27 23:27:03
cos36-cos72
=-2sin54sin(-18)这一步看不懂
=2sin54sin18
=2cos36sin18
=2cos36sin18cos18/cos18
=cos36sin36/cos18
=sin72/(2cos18)
=sin72/(2sin72)=1/2

cos36-cos72

=cos(54-18)-cos(54+18)

=cos54cos18+sin54sin18-[cos54cos18-sin54sin18]
=2sin54sin18

=-2sin54sin(-18)
=2sin54sin18
=2cos36sin18
=2cos36sin18cos18/cos18
=cos36sin36/cos18
=sin72/(2cos18)
=sin72/(2sin72)=1/2

你看不懂那步是用积化和差公式中的这条：
cosθ-cosφ=-2sin[(θ+φ)/2]sin[(θ-φ)/2]

cos36-cos72
=sin54-sin18
=sin(36+18)-sin(36-18)

展开即可