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sin3xCos3x

解: -6sin3xcos3x =-3(2sin3xcos3x) =-3sin6x

这是复合函数求导 Sin3x的导数=(sin3x)'=cos3x×(3x)'=3cos3x

2sin3xcos4x=sin(3x+4x)+sin(3x-4x)=sin7x-sinx ∴sin3xcos4x=(sin7x-sinx)/2 =>∫sin3xcos4xdx=∫(sin7x-sinx)/2dx =∫(sin7x)/2dx-∫(sinx)/2dx =-(cos7x)/14+(cosx)/2+C

y=1/2sin3xcos3x=1/4sin6x 周期T=2π/6=π/3 因为1/4sin(-6x)= -1/4sin6x 即f(-x)=-f(x) 所以是奇函数。

cos3x=cos(2x+x)=cos2xcosx-sin2xsinx =[(cosx)^2-(sinx)^2]cosx-2sinxcosxsinx =(cosx)^3-(sinx)^2cosx-2(sinx)^2cosx =(cosx)^3-3(sinx)^2cosx sin3x=sin(2x+x)=sin2xcosx+cos2xsinx =2sinxcosxcosx+[(cosx)^2-(sinx)^2]sinx =2sinx(cosx)^2+(...

这是辅助角公式

(sin3xcos3x)' =(1/2*sin6x)' =1/2*cos6x*(6x)' =3cos6x

sin6x t等与三分之π

1.f(x)=(sinx+sin3x)/(cosx+cos3x) =(sinx+3sinx-4sin^3 x)/(cosx+4cos^3 x-3cosx) =(4sinx-4sin^3 x)/(4cos^3 x-2cosx) =[4sinx(1-sin^2 x)]/[2cosx(cos^2 x-1)] =(4sinxcos^ x)/(2cosxcos2x) =(2sin2xcosx)/(2cosxcos2x) =tan2x T=π/2 2.f(x)=...

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