题目

求cos(π/11)cos(2π/11)cos(3π/11)cos(4π/11)cos(5π/11)
求值:cos(π/11)cos(2π/11)cos(3π/11)cos(4π/11)cos(5π/11)
(5/24)(11/24)=5/11?,而且过程和题好像都没关系。

提问时间：2020-11-30

答案

cos(π/11)cos(2π/11)cos(3π/11)cos(4π/11)cos(5π/11)
=[2sin(π/11)cos(π/11)cos(2π/11)cos(3π/11)cos(4π/11)cos(5π/11)]/2sin(π/11)
=[sin(2π/11)cos(2π/11)cos(3π/11)cos(4π/11)cos(5π/11)]/2sin(π/11)
=[sin(4π/11)cos(3π/11)cos(4π/11)cos(5π/11)]/4sin(π/11)
=[sin(8π/11)cos(3π/11)cos(5π/11)]/8sin(π/11)
=[sin(3π/11)cos(3π/11)cos(5π/11)]/8sin(π/11)
=[sin(6π/11)cos(5π/11)]/16sin(π/11)
=[sin(5π/11)cos(5π/11)]/16sin(π/11)
=sin(10π/11)]/32sin(π/11)
=1/32