求cos7`+cos47`+cos87`+···+cos327`=

求cos7`+cos47`+cos87`+···+cos327`=
求cos7`+cos47`+cos87`+···+cos327`=

求cos7`+cos47`+cos87`+···+cos327`=
详细步骤：
由余弦的和差化积：
cos α+cos β=2cos[(α+β)/2]·cos[(α-β)/2]
得,
cos7°+cos327°=2cos167°·cos160°
cos47°+cos287°=2cos167°·cos120°
cos87°+cos247°=2cos167°·cos80°
cos127°+cos207°=2cos167°·cos40°
cos167°=2cos167°·(1/2)
所以,
cos7°+cos47°+cos87°+……+cos327°
=2cos167°·(cos160°+cos120°+cos80°+cos40°+(1/2))
=2cos167°·(cos160°+cos80°+cos40°)
=2cos167°·(cos160°+2cos60°cos20°)（和差化积）
=2cos167°·(-cos20°+cos20°)
=0