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sin4xsin8x

∫ sin4x sin8x dx= ∫ (1/2)[cos(8x - 4x) - cos(4x + 8x)] dx= (1/2)∫ (cos4x - cos12x) dx= (1/2)(1/4 sin4x - 1/12 sin12x) + C= (sin4x)/8 - (sin12x)/24 + C

-1/4cos2x用简单的分步积分便可,当然熟练后这个一看就知道了

sin^8x+cos^8x= =(sin^4x-cos^4x)^2+2sin^4xcos^4x =[(sin^2x-cos^2x)(sin^2x+cos^2x)]^2+2sin^4Xcos^4x =(sin^2x-cos^2x)^2+2sin^4Xcos^4x =sin^4x-2sin^2Xcos^2x+cos^4x+2sin^4Xcos^4x=sin^4x+cos^4x+2sin^4Xcos^4x-2sin^2Xcos^2x=(sin^4x+

解:∫(sinx)^8dx=∫((sinx)^2)^4dx =∫((1-cos(2x))/2)^4dx (应用倍角公式) =∫(1-4cos(2x)+6(cos(2x))^2-4(cos(2x))^3+(cos(2x))^4)dx =∫(1-4cos(2x)+6(cos(2x))^2+(cos(2x))^4)dx-4∫(cos(2x))^3dx =∫(1-4cos(2x)+3(1+cos(4x))+((1+cos(4x))/2)^2)dx-4∫(cos(2x)

我来回答sin[θ-(3π/2)]=cos(2π-θ)=cos(-θ)=cosθ告诉你一个正弦和余弦转化的秘诀就是sin(a)=cos(π/2-a),两个角度之和是π/2{sin(θ-5π)cos[(-π/2)-θ]cos(8π-θ)}/sin[θ-(3π/2)]sin(-θ-4π)=-sin(θ)* -sin(θ)* cos(θ) /cos(θ) * -sin(θ)=-sinθ

解cos2xcos4xcos8x=2sin2xcos2xcos4xcos8x/(2sin2x)=sin4xcos4xcos8x/(2sin2x)=2sin4xcos4xcos8x/(2*2sin2x)=sin8xcos8x/(4sin2x)=2sin8xcos8x/(2*4sin2x)=sin16/(8sin2x)

cos^8 x-sin^8 x=(cos^4 x-sin^4 x)(cos^4 x+sin^4 x)cos^4 x-sin^4 x=(cos^2 x-sin^2 x)(cos^2x+sin^2 x)=cos2xcos^4 x+sin^4 x=(cos^2x+sin^2 x)^2-2cos^2x*sin^2 x=1-(sin2x)^2/2所以cos^8 x-sin^8 x=cos2x-cos2x(sin2x)^2/2=cos2x-(sin4xsin2x)/4所以1/4sin2x*sin4x-sin^8 x+cos^8 x=1/4sin2x*sin4x+cos2x-(sin2xsin4x)/4=cos2x

1)已知:f、g的周期都是:Tf(x+T)=f(t)g(x+T)=g(t)h(t)=f(t)+g(t)h(t+T)=f(t+T)+g(t+T)=f(t)+g(t)=h(t)那么f+g的周期还是:T.2) sinx 和 cosx 的周期均为:2π; sin^8x 和 cos^8x 的周期都是:π; 那么由1):sin^8x+cos^8x 的周期还是:π3)化简: sin^8x+

cos^8x-sin^8x+1/4sin2xsin4x-cos2x=(cos^4x+sin^4x)(cos^4x-sin^4x)+1/2sin2xcos2x-cos2x=(cos^4x+sin^4x)(cosx-sinx)+2sinxcosx(cosx-sinx)-cos2x=cos^6x-sin^6x+sinxcos^4x-sin^4xcosx-cos2x=cos^4x-sin^4x-cos2x=cosx-sinx-cos2x=cos2x-cos2x=0所以cos^8x-sin^8x+1/4sin2xsin4x-cos2x=0cos^8x-sin^8x+1/4sin2xsin4x =cos2x

cos(A+B)=cosAcosB-sinAsinBcos(A-B)=cosAcosB+sinAsinBcos(A+B)-cos(A-B)=-2sinAsinBsin4xsin(4x+60)=-1/2{cos(8x+60)-cos(-60)}=-1/2{cos(8x+60)-1/2}=1/2{1/2-cos(8x+60)}]=1/4-1/2cos(8x+60)单调增区间2k∏≤8x+∏/3≤∏+2k∏-∏/24+k∏/4≤x≤∏/12+k∏/4单调减区间-∏+2k∏≤8x+∏/3≤2k∏-∏/6+k∏/4≤x≤-∏/24+k∏/4

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