怎么化解cosx+cos2x+.+cosnx同上

来源:学生作业帮助网 编辑:六六作业网 时间:2024/10/05 23:08:26
怎么化解cosx+cos2x+.+cosnx同上怎么化解cosx+cos2x+.+cosnx同上怎么化解cosx+cos2x+.+cosnx同上cosx+cos2x+.+cosnx=1/2sin(x/

怎么化解cosx+cos2x+.+cosnx同上
怎么化解cosx+cos2x+.+cosnx
同上

怎么化解cosx+cos2x+.+cosnx同上
cosx+cos2x+.+cosnx
=1/2sin(x/2)*(cosx*2sin(x/2)+cos2x*2sin(x/2)+.+cosnx*2sin(x/2))
=1/2sin(x/2)*(sin(3x/2)-sin(x/2)+sin(5x/2)-sin(3x/2)+.+sin(n+1/2)x-sin(n-1/2)x)
=1/2sin(x/2)*(sin(n+1/2)x-sin(x/2))
=1/2sin(x/2)*(2*sinnx*cos(n+1)x)
=(sinnx*cos(n+1)x)/sin(x/2)
或用,[sin(n+1/2)x/sin(x/2)]/2-1/2