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sin²18°+Cos²18°= 给出过程

sin108°=sin(90°+18°)=cos18° cos54°=sin36° 4cos³18°-3cos18°=2sin18°cos18° 同除以cos18° 4cos²18°-3=2sin18° 4(1-sin²18°)-3=2sin18° 所以 4sin²18°+2sin18°+1=0 解方程,sin18°=(-1+√5)/4 cos²18°=1-sin²18°=1...

cos(54°) = 0.58778525229247

sin108°=sin(90°+18°)=cos18° cos54°=sin36° 4cos³18°-3cos18°=2sin18°cos18° 同除以cos18° 4cos²18°-3=2sin18° 4(1-sin²18°)-3=2sin18° 所以 4sin²18°+2sin18°+1=0 解方程,sin18°=(-1+√5)/4 cos²18°=1-sin²18°=...

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∫cos³x/(1+sin²x)dx=∫cos²x/(1+sin²x)dsinx =∫(1-sin²x)/(1+sin²x)dsinx =∫2/(1+sin²x)-1dsinx =2arctansinx-sinx+C

cos平方75°+cos平方15° =sin²15°+cos²15° =1

(sin²80°-sin²10°)²+cos²70° =(cos²10°-sin²10°)²+cos²70° =(cos20°)²+cos²70° =cos²20°+cos²70° =sin²70°+cos²70° =1

cos⁶t+sin⁶t =(cos²t+sin²t)(cos⁴t-cos²tsin²t+sin⁴t) =1×[(cos²t+sin²t)²-3sin²tcos²t] =1×[1²-¾(sin2t)²] =1- ⅜(1-cos4t) =⅝+⅜cos4t

左边=[2-4cos2A+2(cos2A)^2]/[2+4cos2A+2(cos2A)^2]=[1-cos2A]^2/[1+cos2A]^2= [2(sinA)^2]^2/[2(cosA)^2]^2=tanA四次方=右边

记18°=t 则5t=90° sin3t=cos2t sin(t+2t)=cos2t sintcos2t+costsin2t=cos2t sint(1-2sin²t)+2sint(1-sin²t)=1-2sin²t 记sint=x,则 x(1-2x²)+2x(1-x²)=1-2x² (x-1)(4x²+2x-1)=0 x≠1,所以4x²+2x-1=0,取正...

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