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

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/30 18:12:47
cos36°-cos72°=?cos36-cos72=-2sin54sin(-18)这一步看不懂=2sin54sin18=2cos36sin18=2cos36sin18cos18/cos18=cos36sin36/cos18 =sin72/(2cos18)=sin72/(2sin72)=1/2
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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

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
=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

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