求和Sn=cosx+cos2x+cos3x+……+cosnx

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求和Sn=cosx+cos2x+cos3x+……+cosnx
求和Sn=cosx+cos2x+cos3x+……+cosnx

求和Sn=cosx+cos2x+cos3x+……+cosnx
2sin(x/2)[cosx+cos2x+cos3x+……+cosnx ]
=2sin(x/2)cosx+2sin(x/2)cos2x+2sin(x/2)cos3x+……+2sin(x/2)cosnx
=sin(3x/2)-sin(x/2)+sin(5x/2)-sin(3x/2)+sin(7x/2)-sin(5x/2)+……+sin(x/2+nx)-sin(nx-x/2)
=sin(x/2+nx)-sin(x/2)
所以 cosx+cos2x+cos3x+……+cosnx
=[sin(x/2+nx)-sin(x/2)]/[2sin(x/2)]
=sin(x/2+nx)/[2sin(x/2)]-1/2

过程楼上给了。我再补充下
和差化积
sinθ+sinφ = 2 sin[(θ+φ)/2] cos[(θ-φ)/2]
sinθ-sinφ = 2 cos[(θ+φ)/2] sin[(θ-φ)/2]

求和Sn=cosx+cos2x+cos3x+……+cosnx 已知tan2x=-2根号2求cosx(cos3分之2π-cos2x)分之2cosx(cos2π/3-cos2x)分之2cos平方x/2-SINX-1 COS2X=-COSX 为什么cos2x=cosx*cosx-sinx*sinx cosx+cos2x+cos3x+.+cosnx= 求和1 +(1/2)*cosx+ (1/4)*cos2x +… +(1/2∧n)cosnx （1+cos2x)/2cosx=sin2x/(1-cos2x) 求和Sn=1-2 3-4+ 数列Bn=1/n,求和Sn sinX+cosX=1/2,cos2X=? 为什么cos2X=(cosX)^2-(sinX)^2 y=cosx*cos2x的导数是多少 cos2x/sinx+cosx + 2sinx= cos2x+cosx=0,则sin2x+sinx 为什么cos2x=cosx^2-sinx^2 2(cosx)^2-1=cos2x为什么 y=cos2x+sinx(sinx+cosx) 化简 (cosx)^2-(sinx)^2=cos2x?