cosπ/7cos2π/7cos4π/7cos8π/7=?每步都写
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/26 00:35:18
cosπ/7cos2π/7cos4π/7cos8π/7=?每步都写
原式=16sinπ/7cosπ/7cos2π/7cos4π/7cos8π/7/(16siπ/7)
=8sin2π/7cos2π/7cos4π/7cos8π/7/(16siπ/7)
=4sin4π/7cos4π/7cos8π/7/(16siπ/7)
=2sin8π/7cos8π/7/(16siπ/7)
=sin16π/7/(16siπ/7)
=sin2π/7/(16sinπ/7)
=2sinπ/7cosπ/7/(16sinπ/7)
=(cosπ/7)/8
=8sin2π/7cos2π/7cos4π/7cos8π/7/(16siπ/7)
=4sin4π/7cos4π/7cos8π/7/(16siπ/7)
=2sin8π/7cos8π/7/(16siπ/7)
=sin16π/7/(16siπ/7)
=sin2π/7/(16sinπ/7)
=2sinπ/7cosπ/7/(16sinπ/7)
=(cosπ/7)/8
cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15
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