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Cos72°*Cos36°=?

第一步,分子分母同时乘2sin36。第二部,由二倍角公式得2sin36cos36=sin72。第三步,分子分母同时乘以2。第四步,由二倍角公式2sin72cos36=sin144。第五步,sin144=sin(180-36)=sin36。最后约分得出结果

做等腰三角形ABC,其中∠A=36° 易得∠B=∠C=72° 过A做AD⊥BC于D,∵∠B=∠C ∴BC = 2BD cos72°=cos∠B=BD/AB=BC/2AB 过C做∠C的角平分线交AB于E点. ∠ACE=1/2∠C=36°=∠A ∴CE=AE ∵∠BEC是△AEC的外角 ∴∠BEC=∠A+∠ACE=72°=∠B ∴CE=BC ∵∠ACE=∠A,∠BEC=∠B ∴△ABC∽△CEB ∴A...

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

=(sin36*cos72*cos36)/sin36=(1/2sin72*cos72)/sin36=(1/4sin36)/sin36=1/4

解答: 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° =-(1/2)sin144°/sin36° =-(1/2)sin(180°-3...

cos36°-cos72° =2sin54°*sin18° =2sin72°*sin18°*2*sin36°*sin54°/(2*sin36°*sin72°) =(2cos18°*sin18°)*(2sin36°*cos36°)/(sin36°*sin72°) =sin36°*sin72°/(2*sin36°*sin72°) =1/2

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COS72COS36 =2sina36COS72COS36/2sina36 =sin72cos72/2sin36 =2sin72cos72/4sin36 =sin144/4sin36 =sin36/4sin36 =1/4

cos36-cos72 解1. Cos36-cos72 =(sin36cos36-sin36cos72)/sin36 =-(sin108-sin36-sin72)/2sin36 =-(sin72-sin36-sin72)/2sin36 =sin36/2sin36 =1/2 解2. cos36-cos72 =cos(54-18)-cos(54+18) =cos54cos18+sin54sin18-[cos54cos18-sin54sin18] =2...

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