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sinxsin2xsin3x怎么变换到(Cosx%Cos3x)sin3x

利用积化和差公式: sinXsin2Xsin3X = -(1/2)(cos3X-cosX)sin3X 满意请采纳,谢谢!

第一步,(1-cosxcos2xcos3x一直乘到cosnx)和二分之一倍的(1平方 加 2平方 加加加加到 n平方)倍的x平方 是等价无穷小,具体的证明你可以用 ln(1加x)和x 这对等价无穷小(PS:这么代换有很大的好处,大家去试一下就明白了) 去证,,,不明白的...

请看图

sin3x=sin(x+2x)=sinxcos2x+sin2xcosx =(sinx-2(sinx)^3)+2sinx-2(sinx)^2 =3sinx-4(sinx)^3 cos3x=cos(x+2x)=cosxcos2x - sinxsin2x =2(cosx)^3-cosx +2(cosx)^3-2cosx =4(cosx)^3-3cosx (3sinx+sin3x) / (3cosx+cos3x) = [6sinx-4(sinx)^3]/ [...

因为cosX- cos3X =cos(2x-x)-cos(2x+x) =cos2xcosx+sin2xsinx -(cos2xcosx-sin2xsinx) =2sin2xsinx

sin4xsin2x=-1/2[cos(4x+2x)/2-cos(4x-2x)/2]=-1/2(cos3x-cosx) sinxsin3x=-1/2[cos(x+3x)/2-cos(x-3x)/2]=-1/2(cos2x-cosx) sin4xsin2x-sinxsin3x =[-1/2(cos3x-cosx)]-[-1/2(cos2x-cosx)] =1/2(cos2x-cos3x) =1/2*[(-2)sin(2x+3x)sin(2x-3x)] ...

(1) a.b =(cos3x/2,sin3x/2).(cosx/2,-sinx/2) =(cos3x/2)(cosx/2)-(sin3x/2)(sinx/2) = cos2x a+b= (cos3x/2+cosx/2, sin3x/2-sinx/2) |a+b|^2 =(cos3x/2+cosx/2)^2+(sin3x/2-sinx/2)^2 =2+2cos3x/2cosx/2-2sin3x/2sinx/2 =2+cos2x |a+b|=)√(2+...

y=sin²3x+5cosx² y'=(2sin3x)*(cos3x)*3-5(sinx²)*(2x) =3sin6x-10xsinx² 如果题目为 y=sin²3x+5cos²x y'=(2sin3x)*(cos3x)*3-5*(2cosx)(sinx) =3sin6x-5sin2x

证:(1)|sin2x|=|2sinx?cosx|=2|sinx|?|cosx|. ∵|cosx|≤1, ∴|sin2x|≤2|sinx|;(2)当n=1时,结论显然成立.假设当n=k时结论成立,即|sinkx|≤k|sinx|.当n=k+1时, |sin(k+1)x| =|sinkx?cosx+coskx?sinx|≤|sinkx?cosx|+|coskx?sinx| =|sin...

cosx-cos3x=cosx-[cos2xcosx-sin2xsinx] =cosx-cos2xcosx+sin2xsinx =cosx(1-cos2x)+sin2xsinx =cosx*2sin^2x+sin2xsinx =sin2xsinx+sin2xsinx =2sin2xsinx

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