求值:cosπ/17cos2π/17cos4π/17cos8π/17

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求值:cosπ/17cos2π/17cos4π/17cos8π/17
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求值:cosπ/17cos2π/17cos4π/17cos8π/17
求值:cosπ/17cos2π/17cos4π/17cos8π/17

求值:cosπ/17cos2π/17cos4π/17cos8π/17
cos(π/17)cos(2π/17)cos(4π/17)cos(8π/17)
=[16sin(π/17)cos(π/17)cos(2π/17)cos(4π/17)cos(8π/17)]/16sin(π/17)
=[8sin(2π/17)cos(2π/17)cos(4π/17)cos(8π/17)]/16sin(π/17)
=[4sin(4π/17)cos(4π/17)cos(8π/17)]/16sin(π/17)
=[2sin(8π/17)cos(8π/17)]/16sin(π/17)
=sin(16π/17)/16sin(π/17)
=1/16