cos（π/11）cos（2π/11）cos（3π/11）cos（4π/11）cos（5π/11）怎么解

题目

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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