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cosπ/15cos2π/15cos4π/15cos8π/15=
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答案和解析
cos(π/15)cos(2π/15)cos(4π/15)cos(8π/15)
=[16sin(π/15)cos(π/15)cos(2π/15)cos(4π/15)cos(8π/15)]/16sin(π/15)
=[8sin(2π/15)cos(2π/15)cos(4π/15)cos(8π/15)]/16sin(π/15)
=[4sin(4π/15)cos(4π/15)cos(8π/15)]/16sin(π/15)
=[2sin(8π/15)cos(8π/15)]/16sin(π/15)
=sin(16π/15)/16sin(π/15)
=sin(π+π/15)/16sin(π/15)
=-sin(π/15)/16sin(π/15)
=-1/16
=[16sin(π/15)cos(π/15)cos(2π/15)cos(4π/15)cos(8π/15)]/16sin(π/15)
=[8sin(2π/15)cos(2π/15)cos(4π/15)cos(8π/15)]/16sin(π/15)
=[4sin(4π/15)cos(4π/15)cos(8π/15)]/16sin(π/15)
=[2sin(8π/15)cos(8π/15)]/16sin(π/15)
=sin(16π/15)/16sin(π/15)
=sin(π+π/15)/16sin(π/15)
=-sin(π/15)/16sin(π/15)
=-1/16
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