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一道数学题计算:cosπ/17*cos2π/17*cos4π/1
发表于：2024-10-24 00:00:00浏览：7次
问题描述：计算:cπ/17*cos2π/17*cos4π/17*cos8π/17=
cos(π/17)cos(2π/17)cos(4π/17)cos(8π/17)
=[1/2sin(π/17)][2sin(π/17)cos(π/17)]cos(2π/17)cos(4π/17)cos(8π/17)
=1/[2sin(π/17)]sin(2π/17)cos(2π/17)cos(4π/17)cos(8π/17)
=[1/4sin(π/17)]sin(4π/17)cos(4π/17)cos(8π/17)
=[1/8sin(π/17)sin(8π/17)cos(8π/17)
=[1/16sin(π/17)]sin(16π/17)
=(1/16)[sin(16π/17)/sin(π/17)]
=(1/16)[sin(π/17)/sin(π/17)]
=1/16.
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