作业帮求和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]
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