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  • 求cos(π/11)cos(2π/11)cos(3π/11)cos(4π/11)cos(5π/11)

    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?,而且過程和題好像都沒關(guān)系。
    數(shù)學(xué)人氣:957 ℃時間:2020-08-22 14:00:06
    優(yōu)質(zhì)解答
    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
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