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sin18 Cos72

sin72*cos18 +cos72*sin18 =sin72*sin(90-18) +cos72*cos(90-18) =(sin72)^2 +(cos72)^2 =1

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

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

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

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

∵ AB ? AC =cos18°?2cos63°+cos72°?2cos27°=2(cos18°sin27°+sin18°cos27°)=2sin(18°+27°)=2sin45°= 2 , | AB | = co s 2 18°+co s 2 72° = co s 2 18°+ sin 2 18° =1, | AC | = 4co s 2 63°+4co s 2 27° = 4(si n 2 27°+co s 2 27°) =2,...

cos18*cos36*cos72*cos144 上下同乘以16sin18 =16*sin18*cos18*cos36*cos72*cos144/(16sin18) 反复运用2sinacosa=sin2a =8sin36cos36cos72cos144/(16sin18) =4sin72cos72cos144/(16sin18) =.. =sin288/(16sin18) 因为:sin(360-a)=-sina =-sin72...

由题意得,AB=(cos18°,cos72°)=(cos18°,sin18°),则|AB|=1BC=(2cos63°,2cos27°)=(2cos63°,2sin63°),则|BC|=2,∵AB?BC=2cos63°cos18°+2sin63°sin18°=2cos(63°-18°)=2cos45°=2,∴cos<AB,BC>=AB?BC|AB||BC|=22,即<AB,BC>=45°...

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