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Cos36°+Cos72°=______

∵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...

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

原式=(sin36°cos36°cos72°)/sin36° =(1/2sin72°cos72°)/sin36° =(1/4sin144°)/sin36° =1/4(sin36°/sin36°) =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...

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°) ...

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

解: cos36°-cos72° =sin54°-sin18° =sin(36°+18°)-sin(36°-18°) =sin36°cos18°+cos36°sin18°-sin36°cos18°+cos36°sin18° =2cos36°sin18° =2cos36°sin18°cos18°/cos18° =cos36°sin36°/cos18° =sin72°/2cos18° =cos18°/2cos18° =1/2

数理答疑团为您解答,希望对你有所帮助。 此种方法简单易解。 祝你学习进步,更上一层楼! (*^__^*)

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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