化简cosπ/7*cos2π/7*cos4π/7
提示:据分析应该用倍角公式.
人气:144 ℃ 时间:2020-03-19 08:33:13
解答
cos(π/7)*cos(2π/7)*cos(4π/7)
=[2sin(π/7)cos(π/7)*cos(2π/7)*cos(4π/7)]/2sin(π/7)
=[sin(2π/7)*cos(2π/7)*cos(4π/7)]/2sin(π/7)
=[2sin(2π/7)*cos(2π/7)*cos(4π/7)]/4sin(π/7)
=[sin(4π/7)*cos(4π/7)]/4sin(π/7)
=[2sin(4π/7)*cos(4π/7)]/8sin(π/7)
=sin(8π/7)/8sin(π/7) (因为sin(8π/7)=-sin(π/7))
=-1/8
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