cosxcos2xcos3x =1/2(cosx+cos3x)cos3x =1/4(cos2x+cos4x+cos6x+1)=1/4{[1-2x^2+o1(x^2)]+[1-8x^2+o2(x^2)]+[1-18x^2+o3(x^2)]+1} =1-7x^2+o(x^2)∴a=7，n=2
化简:cosx+cos2x+cos3x+……cosnx=?化为最简式应该为什么呢? 相关知识点: 试题来源: 解析 乘以2sinx, 积化和差就变成了 sin2x-0+sin3x-sinx+sin4x-sin2x+...+ sinnx-si(n-2)x+sin(n+1)x-sin(n-1)x =sin(n+1)x+sinnx-sinx 再除以2sinx,即为答案,[sin(n+1)x+sinnx-sinx]/2sinx ...
1-cosxcos2xcos3x = 1 - [1-(1/2)x^2-(1/2)(2x)^2-(1/2)(3x)^2 + o(x^2)]= (1/2)(1+4+9)x^2 + o(x^2) = 7x^2 + o(x^2)
0.5+cosx+cos2x+cos3x………cosnx,把这个式子化简成分子和分母的形式 答案 把原式乘以sinx后再除以sinx原式={1/2(sinx)+1/2(sin2x-sin0)+1/2(sin3x-sinx)+1/2(sin4x-sin2x)+………+1/2[sin(n+1)x-sin(n-1)x]}/sinx=1/2[sin(nx)+sin(n+1)x]/sinx=sin{[(2n+1)/2]x}cos(x/2...
答案 求3cosx+cos2x+cos3x 我一个一个分解,你顺便记记公式,我还是喜欢用α,还是用α给你做好了 cos3α=cos(2α+α) =cos2α·cosα-sin2α·sinα =(cosα^2-sinα^2)cosα-2sinα^2·cosα =[cosα^2-(1-cosα^2)]cosα-...相关推荐 1数学三角函数化简3cosx+cos2x+cos3x 反馈...
希望你能看懂 张宇的1000题里用过这个
sinnxsin(x 2)=1 2(cos(nx+x 2)-cos(nx-x 2))=1 2(cos2n+1 2-cos2n-1 2)以上各式相加得sinx 2S=1 2(cos2n+1 2-cosl X),所以原式=1 1 cos(n+-)x-cos-x 2 2 2sin 2=n+l nx sin xsin 2 2 sin- 2(2)设S=cosx+cos2x+cos3x+…+cosnx,将式子两边乘以sinx 2,cosxsinx 2...
(cos7/2x-cos5/2x) insn()- 1/2(cos(nx+x/2)-cos(nx-x/2))=1/2(cos(2n+1)/2x-cos(2n-1)/2x) 以上各式相加得s lnx/2S=1/2(cos(2n+1)/2x-cos1/2x)所以原式(cos(n+1/2)x-cos1/2x)/x (sin(n+1)/2πsinπ/(2))/(sinπ/(2)) 2)设S=cosx+cos2x+cos3x+..+cosnx...
= 2 sinx*cosx*cos2x*cos4x / (2sinx)= sin2x * cos2x *cos4x /(2sinx) =...= sin8x / (8sinx)cos3x*cos5x =(1/2) ( cos8x +cos2x)原式= (1/16) (1/sinx) [ sin8x cos8x + sin8xcos2x ]= (1/32) (1/sinx) [ sin16x + sin10x +sin6x ]