高考问答泰国男星Diew:一道三角函数数学题～
来源：百度文库 编辑：高考问答 时间：2024/05/06 08:46:45
计算cos(π/17)cos(2π/17)cos(4π/17)cos(8π/17)
要求有过程有思路，，不然看不懂．．－ －
要求有过程有思路，，不然看不懂．．－ －
原式=cos(π/17)cos(2π/17)cos(4π/17)cos(8π/17)
=cos(π/17)cos(2π/17)cos(4π/17)cos(8π/17)*sin(π/17)/sin(π/17)
=[2sin(π/17)cos(π/17)]cos(2π/17)cos(4π/17)cos(8π/17))/2sin(π/17)
=sin(2π/17)cos(2π/17)cos(4π/17)cos(8π/17))/2sin(π/17)
=sin(4π/17)cos(4π/17)cos(8π/17))/4sin(π/17)
=sin(8π/17)cos(8π/17))/8sin(π/17)
=sin(16π/17)/16sin(π/17)
=sin(π-π/17)/16sin(π/17)
=sin(π/17)/16sin(π/17)
=1/16
原式=sin(π/17)cos(π/17)cos(2π/17)cos(4π/17)cos(8π/17)/sin(π/17)
反复利用2倍角公式得
原式=1/16*(sin(16π/17)/sin(π/17))=1/16
乘以Sin(π/17)再把它除掉
运用2倍角公式
那么cos(π/17)
和Sin(π/17)
就会得到1/2
Sin(2π/17)
一直这样下去
最后就会得到Sin(16π/17)/16Sin(π/17) =1/16