百度作业网求和Sn=cosx+cos2x+cos3x+……+cosnx
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/07/08 22:05:58
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
=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
求和Sn=cosx+cos2x+cos3x+……+cosnx
化简：cosx+cos2x+cos3x+……cosnx=?
cosx+cos2x+cos3x+.+cosnx=
0.5+cosx+cos2x+cos3x…………cosnx,把这个式子化简成分子和分母的形式
COSX+COS2X+COS3X+COS4X+COS5X+COS6X+...+COSNX=1/2|{SIN(N+1/2)
求证：cosx+cos2x+…+cosnx=cosn+12x•sinn2xsinx2
怎么化解cosx+cos2x+.+cosnx
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