您的位置: 首页  >  作业答案  >  其他  >  cos36°-cos72°=?cos36-cos72=-2sin54sin(-18)这一步看不懂=2sin54sin18=2cos36sin18=2cos36sin18cos18/cos18=cos36sin36/cos18 =sin72/(2cos18)=sin72/(2sin72)=1/2

cos36°-cos72°=?cos36-cos72=-2sin54sin(-18)这一步看不懂=2sin54sin18=2cos36sin18=2cos36sin18cos18/cos18=cos36sin36/cos18 =sin72/(2cos18)=sin72/(2sin72)=1/2

分类: 作业答案 • 2022-05-20 20:29:15
问题描述：

cos36°-cos72°=?
cos36-cos72
=-2sin54sin(-18)这一步看不懂
=2sin54sin18
=2cos36sin18
=2cos36sin18cos18/cos18
=cos36sin36/cos18
=sin72/(2cos18)
=sin72/(2sin72)=1/2

答

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

答

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]

答

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

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