作业帮这个怎么化简?
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/07/05 23:52:04
这个怎么化简?
sin(pi/18)sin(5pi/18)sin(-65pi/18)=sin(pi/18)sin(5pi/18)sin(-4pi+7pi/18)
=sin(pi/18)sin(5pi/18)sin(7pi/18)=cos(pi/2-pi/18)cos(pi/2-5pi/18)cos(pi/2-7pi/18)
=cos(4pi/9)cos(2pi/9)cos(pi/9)=2sin(pi/9)cos(pi/9)cos(2pi/9)cos(4pi/9)/[2sin(pi/9)]
=sin(2pi/9)cos(2pi/9)cos(4pi/9)/[2sin(pi/9)]=2sin(2pi/9)cos(2pi/9)cos(4pi/9)/[4sin(pi/9)]
=sin(4pi/9)cos(4pi/9)/[4sin(pi/9)]=2sin(4pi/9)cos(4pi/9)/[8sin(pi/9)]
=sin(8pi/9)/[8sin(pi/9)]=sin(pi-pi/9)/[8sin(pi/9)]=sin(pi/9)/[8sin(pi/9)]=1/8
=sin(pi/18)sin(5pi/18)sin(7pi/18)=cos(pi/2-pi/18)cos(pi/2-5pi/18)cos(pi/2-7pi/18)
=cos(4pi/9)cos(2pi/9)cos(pi/9)=2sin(pi/9)cos(pi/9)cos(2pi/9)cos(4pi/9)/[2sin(pi/9)]
=sin(2pi/9)cos(2pi/9)cos(4pi/9)/[2sin(pi/9)]=2sin(2pi/9)cos(2pi/9)cos(4pi/9)/[4sin(pi/9)]
=sin(4pi/9)cos(4pi/9)/[4sin(pi/9)]=2sin(4pi/9)cos(4pi/9)/[8sin(pi/9)]
=sin(8pi/9)/[8sin(pi/9)]=sin(pi-pi/9)/[8sin(pi/9)]=sin(pi/9)/[8sin(pi/9)]=1/8