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