cos(pai/17)cos(2pai/17)cos(4pai/17)cos(8pai/17)=
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解cos(π/17)cos(2π/17)cos(4π/17)cos(8π/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)
=2sin(2π/17)cos(2π/17)cos(4π/17)cos(8π/17)/2×2sin(π/17)
=sin(4π/17)cos(4π/17)cos(8π/17)/2×2sin(π/17)
=2sin(4π/17)cos(4π/17)cos(8π/17)/2×2×2sin(π/17)
=sin(8π/17)cos(8π/17)/2×2×2sin(π/17)
=2sin(8π/17)cos(8π/17)/2×2×2×2sin(π/17)
=sin(16π/17)/2×2×2×2sin(π/17)
=sin(π/17)/2×2×2×2sin(π/17)
=1/16
=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)
=2sin(2π/17)cos(2π/17)cos(4π/17)cos(8π/17)/2×2sin(π/17)
=sin(4π/17)cos(4π/17)cos(8π/17)/2×2sin(π/17)
=2sin(4π/17)cos(4π/17)cos(8π/17)/2×2×2sin(π/17)
=sin(8π/17)cos(8π/17)/2×2×2sin(π/17)
=2sin(8π/17)cos(8π/17)/2×2×2×2sin(π/17)
=sin(16π/17)/2×2×2×2sin(π/17)
=sin(π/17)/2×2×2×2sin(π/17)
=1/16
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