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Cos72°=多少?

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...

(√(5)-1)/2

cos72°-cos36° =cos(54+18)-cos(54-18) =[cos54cos18-sin54sin18]-[cos54cos18+sin54sin18] =-2sin54sin18 (sin54=cos36) =-2cos36sin18 =-2cos36sin18cos18/cos18 =-cos36sin36/cos18 =-sin72/(2cos18) =-sin72/(2sin72) =-1/2

cos(72°)=0.30901699437495

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

解: sin54°cos72° =cos36°sin18° =cos36°sin18°cos18°/cos18° =cos36°×1/2sin36°/cos18° =1/4sin72°/cos18° =1/4

cos72=cos(2π/5) cos(2π/5)+cos(4π/5)=cos(2π/5)-cos(π/5); 而由积化和差公式: cos(2π/5)+cos(4π/5)=2cos(3π/5)*cos(π/5); 而cos(2π/5)=2cos(π/5)*cos(π/5)-1 由以上三个方程,足够解出cos(2π/5)了。结果就是楼上两位朋友的...

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

cos72°= (√5 - 1) / 4

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