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15度和75度角的sin,Cos,tAn值?

根号下BC的平方加上AC的平方等于AB sin15=BC/AB cos15=AC/AB tan15=BC/AC sin75=AC/AB cos75=BC/AB tan75=AC/BC

sin15°=cos75°=(√6-√2)/4 cos15°=sin75°=(√6+√2)/4 tan15°=cot75°=(√6-√2)/(√6+√2)=(√6-√2)^2/4=2-√3 tan75°=cot15°=(√6+√2)/(√6-√2)=(√6+√2)^2/4=2+√3

因为sin15°= sin(45° - 30°) = sin45°cos30° - cos45°sin30 °= √2/2×√3/2 - √2/2×1/2= (√6 - √2)/4cos15 °= cos(45 °- 30°) = cos45°cos30 °+ sin45°sin30° = √2/2×√3/2 + √2/2×1/2 = (√6+√2)/4tan15°=sin15°/cos15°= (√6 - √2)/ (√6 +√2)=2-√3 ...

sin(75度)=sin(30度+45度) cos(75度)=cos(30度+45度) 两角和公式Sin(A+B)=SinA*CosB+SinB*CosA Sin(A-B)=SinA*CosB-SinB*CosA Cos(A+B)=CosA*CosB-SinA*SinB Cos(A-B)=CosA*CosB+SinA*SinB Tan(A+B)=(TANA+TanB)/(1-TanA*TanB) Tan(A-B)...

等于。

因为........ Sin 15° = b/c = Cos 15°

sin75°×cos75° =1/2sin150° =1/2sin(180-30) =1/2sin30 =1/2*1/2 =1/4

变成sin(45+30)展开算

因为sin15°= sin(45° - 30°) = sin45°cos30° - cos45°sin30 °= √2/2×√3/2 - √2/2×1/2= (√6 - √2)/4cos15 °= cos(45 °- 30°) = cos45°cos30 °+ sin45°sin30° = √2/2×√3/2 + √2/2×1/2 = (√6+√2)/4tan15°=sin15°/cos15°= (√6 - √2)/ (√6 +√2)=2-√3 ...

上式 = sin15°cos75°+cos15°sin75°=sin(15°+ 75°) = sin90°= 1

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