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sin18 Cos72

根据正弦定理:sin(A+B)=sinAcosB+cosAsinB即sin72°cos18°+cos72°sin18° =sin(72°+18°) =sin90° =1

根据正弦定理:sin(A+B)=sinAcosB+cosAsinB即sin18cos72+sin72cos18=sin(18+72)=1

sin*72+18)=sin90=1

这是诱导公式

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

原式=cos78°sin72°+sin78°cos72°=sin(78°+72°)=sin150°=1/2

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

cos30°tan30°+sin60°tan45°tan60°+sin18°(sin212°+sin278)cos72°=32×33+32×1×3+cos72°(sin212°+cos212°)cos72°=12+32+1=3.

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