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Cos2x Cosx

∫cos2x/(cosx-sinx)dx =∫(cos²x-sin²x)/(cosx-sinx)dx =∫(cosx+sinx)(cosx-sinx)/(cosx-sinx)dx =∫(cosx+sinx)dx =sinx-cosx+C

简单凑微分方法,详解参考下图

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积化和差公式: 2cosAcosB = cos(A+B)+cos(A-B) 其中A=2x,B=x,代入即可

cos(A+B)=cosA.cosB - sinA.sinB (1) cos(A-B)=cosA.cosB + sinA.sinB (2) (1)+(2) cosA.cosB =(1/2) [ cos(A-B)+cos(A+B) ] A=x , B=2x cosx.cos2x =(1/2) [ cosx+cos(3x) ]

对于Sn=cosx+cos2x+cos3x+……+cosnx,有: 2sin(x/2)[cosx+cos2x+cos3x+……+cosnx ] =2sin(x/2)cosx+2sin(x/2)cos2x+2sin(x/2)cos3x+……+2sin(x/2)cosnx =sin(3x/2)-sin(x/2)+sin(5x/2)-sin(3x/2)+sin(7x/2)-sin(5x/2)+……+sin(x/2+nx)-sin(nx-x/2) ...

解: cos2x=cos(x+x) =cosx*cosx-sinx*sinx =(cosx)^2-(sinx)^2 (上式应用的是cos(x+y)=cosx*cosy-sinx*siny,令x=y)

cos2x的图像横坐标乘两倍,2cosx的图像纵坐标乘两倍

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