问题: 高1数学题4
求cos(派/9)cos(2派/9)cos(3派/9)cos(4派/9)
解答:
cos(π/9)cos(2π/9)cos(3π/9)cos(4π/9)
=2sin(π/9)cos(π/9)cos(2π/9)cos(3π/9)cos(4π/9)/2sin(π/9)
=2sin(2π/9)cos(2π/9)cos(3π/9)cos(4π/9)/4sin(π/9)
=2sin(4π/9)cos(3π/9)cos(4π/9)/8sin(π/9)
=sin(8π/9)cos(3π/9)/8sin(π/9)
=sin(π/9)cos(3π/9)/8sin(π/9)
=cos(3π/9)/8
=1/16
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