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用sinx和Cosx表示Cos6x和sin6x

【硬功夫】两角和公式+二倍角公式 3个基本的2倍角公式:(1) sin2A=2sinAcosA (2) cos2A=2(cosA)^2-1=1-2(sinA)^2 (3) tan2A=2tanA/[1-(tanA)^2] 两角和公式 cos(α+β)=cosαcosβ-sinαsinβ cos(α-β)=cosαcosβ+sinαsinβ sin(α+β)=sinαco...

因为:cos4x+sin4x+sin2xcos2xsin6x+cos6x+2sin2xcos2x=(sin 2x+cos 2x) 2?2sin 2xcos 2x +sin 2xcos 2x (sin 2x+cos 2x) [(sin 2x) 2?sin 2xcos 2x+(cos 2x ) 2]+ 2sin 2xcos 2x =1?sin 2xcos 2x (sin 2x) 2+(cos 2x) 2+sin 2xcos 2x =1?sin 2x...

y=sin^6x+cos^6x =(sin³x+cos³x)(sin⁴x-sin²xcos²x+cos⁴x) =sin⁴x-sin²xcos²x+cos⁴x =(sin²x+cos²x)²-3sin²xcos²x =1-3/4*(2sinxcosx)² =1-3/4sin²2...

利用 e^(ix)=cosx+isinx; e^(ix)+e^(i2x)+e^(i3x)+……+e*(inx)=(cosx+cos2x+……+cosnx)+i(sinx+sin2x+……+sinnx) =[e^(inx+ix) -e^(ix)]/[e^(ix)-1]; 将最后一个等号右端分成实部和虚部(分母和分子同乘以 (cosx-1)-isinx),与等号左端实部和虚部...

方法1y=sin²(3x)y=1/2*(1-cos6x)=1/2-(1/2)cos6xdy/dx=-1/2*d(cos6x)/d(6x)*d(6x)/dx=-1/2*(-sin6x)*6=3sin6x 方法2:直接用链式法则y=sin²(3x)dy/dx=d[sin(3x)]²/d[sin(3x)]*d[sin(3x)]/d(3x)*d(3x)/dx=2sin(3x)*cos(3x)*3=6sin(...

[(cosx)^6]' =6(cosx)^5·(-sinx) =3sin2x(cosx)^4

sin^6x+cos^6x =(sin^2x+cos^2x)(sin^4x+cos^4x-sin^2xcos^2x) =sin^4x+cos^4x-sin^2xcos^2x =(sin^2x+cos^2x)^2-3sin^2xcos^2x =1-3sin^2xcos^2x =1-3/4·(sin2x)^2 =5/8+3/8·cos4x 所以,n阶导数为 3/8·4^n·cos(4x+nπ/2)

积化和差公式: sinαsinβ=-[cos(α+β)-cos(α-β)]/2 cosαcosβ= [cos(α+β)+cos(α-β)]/2 sinαcosβ= [sin(α+β)+sin(α-β)]/2 cosαsinβ= [sin(α+β)-sin(α-β)]/2 sin2x*sin4x=-(cos6x-cos2x)/2 sin2x*cos4x= (sin6x-sin2x)/2 cos2x*sin4x= (sin6x+sin2x)/2

y=sin6x+cos6x=(sin2x+cos2x)(sin4x-sin2xcos2x+cos4x)=1-3sin2xcos2x=1-34sin22x=38cos4x+58.∴T=π2.当cos4x=1,即x=kπ2(k∈Z)时,ymax=1.

sin4x-sin6x的原函数是: -(1/4)cos4x+(1/6)cos6x+C

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