化简求值cos(π/7)cos(2π/7)cos(4π/7)

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化简求值cos(π/7)cos(2π/7)cos(4π/7)

化简求值cos(π/7)cos(2π/7)cos(4π/7)
化简求值cos(π/7)cos(2π/7)cos(4π/7)

化简求值cos(π/7)cos(2π/7)cos(4π/7)
原式=8sin (π/7)cos(π/7)cos(2π/7)cos(4π/7)/8sin(π/7)
=4sin(2π/7)cos(2π/7)cos(4π/7)/8sin(π/7)
=2sin(4π/7)cos(4π/7)/8sin(π/7)
=sin(8π/7)/8sin(π/7)
=-sin(π/7)/8sin(π/7)
=-1/8