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Cos72 Cos36

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

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

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...

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

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

∵cos3α=cos(2α+α)=cos2αcosα-sin2αsinα=(2cos2α-1)cosα-2sin2αcosα=2cos3α-cosα-2(1-cos2α)cosα=4cos3α-3cosα,又cos54°=sin36°∴4cos318°-3cos18°=2sin18°cos18°,∴4cos218°-3=2sin18°,化为4sin218°+2sin18°-1=0,解得sin18°=5?14.∴cos3...

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

2sin36°cos36°=sin(2*36°)=sin72°=sin(180°-72°)=sin108°=sin(3*36°)=3sin36°-4sin??36°=sin36°(3-4sin??36°)=sin36°[3-4(1-cos??36°)]=sin36°(4cos??36°-1)4cos??36°-2cos36°-1=0,cos36°=[2+√(2??+4*4*1)]/(2*4)=(√5+1)/4cos72°cos36°=cos(2*36...

=(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...

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