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sin36°sin54°是什么意思

积化和差公式:sin(a)sin(b) = -1/2*[cos(a+b)-cos(a-b)] 你的问题是求两个正弦函数的积,这两个角度相加为90度,所以可以使用积化和差的公式进行计算,转换为特殊角计算。

用sin2A=2sinAcosA 拼凑即得答案

sin12°sin48°sin54° =(1/2)(cos36°-cos60°)cos36° =(1/2)[(cos36°)^2-(1/2)cos36°] =(1/4)[1+cos72°-cos36°] =(1/4)[1-2sin54°sin18°] =(1/4)[1-2sin54°sin18°cos18°/cos18°] =(1/4)[1-cos36°sin36°/cos18°] =(1/4)[1-sin72°/(2cos18°)] =(1/...

sin54°cos36°+cos54°sin36° =sin(54°+36°) =sin90° =1

sin12°sin48°sin54° =(1/2)(cos36°-cos60°)cos36° =(1/2)[(cos36°)^2-(1/2)cos36°] =(1/4)[1+cos72°-cos36°] =(1/4)[1-2sin54°sin18°] =(1/4)[1-2sin54°sin18°cos18°/cos18°] =(1/4)[1-cos36°sin36°/cos18°] =(1/4)[1-sin72°/(2cos18°)] =(1/...

原式=sin36°-sin36°=0

sin42°-cos12°+sin54° =sin42°-sin78°+sin54° =-2cos60°sin18°+sin54° =sin54°-sin18° =2cos36°sin18° =2cos36°sin18°sin36°/sin36° =sin18°sin72°/sin36° =2sin18°cos18°/2sin36° =sin36°/2sin36° =1/2

sin36°=cos54° tan81°=cot9° 所以原题=cos^254°+sin^254°-cot^9°=1-cot^29°

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

(sin36°+sin15°sin39°)/(cos36°-cos15°sin39°) =[sin36°+(cos24°-cos54°)/2]/[cos36°-(sin54°+sin24°)/2] =(2sin36°+cos24°-sin36°)/(2sin54°-sin54°-sin24°) =(sin36°+cos24°)/(sin54°-sin24°) =(sin36°+sin66°)/(sin54°-sin24°) =(2sin51°cos1...

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