如今小伙伴们关于sinxsin2xsin3x化简真相曝光简直太清晰了，小伙伴们都想要分析一下sinxsin2xsin3x化简，那么夕夕也在网络上收集了一些关于积化和差公式的一些信息来分享给小伙伴们，详情曝光令人惊了个呆，希望能给小伙伴们一些参考。

用积化和差~

sinxsin2xsin3x =1/2(cos2x-cos4x)sin2x =1/4sin4x-1/4(sin6x-sin2x) =1/4(sin4x-sin6x+sin2x) 所以∫sinxsin2xsin3xdx =1/4∫(sin4x-sin6x+sin2x)dx =1/4(-1/4*cos4x+1/6*cos6x-1/.

∫sinxsin2xsin3xdx=∫sinx * (1/2)(cosx-cos5x)dx=(1/2)∫sinxcosxdx - (1/2)∫sinxcos5xdx=(1/2)∫sinxdsinx - (1/4)∫(sinx6x-sin4x)dx=(1/2)(sin²/2) - (1/4)(-1/6)cos6x + (1/4)(-1/4)cos.

设s=sinx+sin2x+sin3x+……+sinnx 两边同乘以2sin(x/2)(x≠2kπ,k∈z) 得2sin(x/2)s=cos(x/2)-cos[(2n+1)x/2]=2sin(nx/2)sin[(n+1)x/2] 所以s=sin(nx/2)sin[(n+1)x/2]÷sin(x/2)

cos(A-B) = cosAcosB+sinAsinB A=3x, B =2x cos2xcox3x-sin2xsin3x=cos(2x+3x)=cos5x

sin2xcos3x =1/2[sin(2x+3x)+sin(2x-3x)] =1/2(sin5x-sinx) 积化和差 根据公式sinacosb=1/2(sin(a+b)+sin(a-b))得sin2xcos3x=1/2(sin(2x+3x)+sin(2x-3x)) =1/2(sin5x+sin(-x)) =(sin5x-sinx)/2.

sinXsin3X=[(cos3XcosX+sinXsin3X)-(cos3XcosX-sinXsin3X)]/2 =[cos(3X-X)-cos(3X+X)]/2 =1/2(cos2X-cos4X)

sinx+2sin2x=3+sin3x sinx-sin3x+2sin2x=3 sin(2x-x)-sin(2x+x)+2sin2x=3 -2sinxcos2x+2sin2x=3 sin2x-sinxcos2x=3/2 后面可以这样: 2sinxcosx-sinx(2cosx平方-1)=3/2 2sinx(cosx-2cosx平方+1)=3/2 sinx(-(osx-1/2)平方-3/4)=3/2 第一项不大于1第二项不大于3/4 且二者不能同时达到.故右边小于3/2

2sinxsin(x+π/3)=2sinx[sinxcos(π/3)+cosxsin(π/3)] =2sinx[(1/2)sinx+(√3/2)cosx] =sin²x+√3sinxcosx =(√3/2)sin2x+(1-cos2x)/2 =-[(1/2)cos2x-(√3/2)sin2x]+1/2 =-cos(2x+π/3)+1/2 所以选A

^y=sinx*sin2x =sinx*2sinx*cosx =2sinx^52612*cosx =2*(1-cosx^2)*cosx u=cosx, u的范围[-1,1] y=2u-2u^3 y'=2-6u^2=0 ==> u^2=1/3==>u=根号41023/3,或者-根号3/3 u=根号3/3时,y最大1653 u=-根号3/3,y最小分回别求出答即可.

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