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Cos72度*Cos36度

cos72°cos36° =2sin36°cos72°cos36°/2sin36° (分子分母同时乘以2sin36°) =sin72°cos72°/2sin36° (2sin a * cos a=sin2a,所以2sin36°cos36°=sin72°) =2sin72°cos72°/4sin36° (分子分母同时乘以2) =sin144°/4sin36° (2sin a * cos a=sin2a,...

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

解:利用二倍角公式sin2a=2sina·cosa和诱导公式sin(180°-a)=sina即可。 cos36°·cos72° =2sin36°·cos36°·cos72°/(2sin36°) =sin72°·cos72°/(2sin36°) =2sin72°·cos72°/(4sin36°) =sin144°/(4sin36°) =sin(180°-36°)/(4sin36°) =sin36°/(4sin36°) ...

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...

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