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sin3x sinx

解:∫sin3XsinXdx =∫-(1/2)[cos(3x+x)-cos(3x-x)]dx =-(1/2)∫(cos4x-cos2x)dx =(-1/2)[(1/4)sin4x-(1/2)sin2x]+C =-(1/8)sin12x+(1/4)sin2x+C 不懂再问懂请采纳

sin3x =sin(2x+x) =sin2xcosx+cos2xsinx =2sinxcosxcosx+cos2xsinx =2sinxcos²x+cos2xsinx sin3x-sin2x+sinx =2sinxcos²x+cos2xsinx-sin2x+sinx=0 若sinx=0 此时x=kπ 若sinx≠0时,得: 2cos^2x+cosx+1=0 相当于一元二次方程2x^2+x+1=0...

记住在x趋于0的时候, sinx就等价于x, 那么这里的sin3x/sinx就 等价于3x/x, 显然极限值就是3

令 f(x)=sin4xsin2x-sinxsin3x=?12(cos6x?cos2x)+12(cos4x?cos2x)=12(cos4x-cos6x),则有f′(x)=3sin6x-2sin4x,令f′(x)=0,可得x=0 或 x=π2,即f′(0)=0,f′(π2)=0,而且还有f′(π)=0.由于f′(x)在x=0的左侧小于0,右侧大于0,故f...

sin3x=sin(x+2x) =sinxcos2x+cosxsin2x =sinx[1-2(sinx)^2]+cosx(2sinxcosx) =sinx[1-2(sinx)^2]+2sinx(cosx)^2 =sinx-2(sinx)^3+2sinx[1-(sinx)^2] =sinx-2(sinx)^3+2sinx-2(sinx)^3 =3sinx-4(sinx)^3 所以 -sin3x=4(sinx)^3-3sinx.

利用积化和差公式-2sin((A+B)/2)*sin((A-B)/2)=cosA-cosB 2sin(x/2)*sinx=cos(x/2)-cos(3x/2) 2sin(x/2)*sin2x=cos(3x/2)-cos(5x/2) ... 2sin(x/2)*sinnx=cos((2n-1)x/2)-cos((2n+1)x/2) 裂项相消 原式就等于cos(x/2)-cos((2n+1)x/2)

本题有问题的,最大值不存在的 sin3x/sinx =(3sinx-4sin³x)/sinx =3-4sin^x≤3 而此时sinx=0,函数无意义的。

sin3x =sin(2x+x) =sin2x×cosx+cos2x×sinx =2×sinx×cosx×cosx+(1-2sin²x)×sinx =2sinx×(1-sin²x)+(1-2sin²x)×sinx =2sinx×(1-sin²x)+(1-2sin²x)×sinx =2sinx-2sin³x+sinx-2sin³x=3sinx-4sin³x

当x趋向于0时sinx趋向于1所以等于三

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