cosπ/11*cos2π/11*cos3π/11*cos4π/11*cos5π/11上式为何等于cosπ/11*cos2π/11*cos4π/11*cos8π/11*cos16π/11

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**cosπ/11cos2π/11cos3π/11cos4π/11cos5π/11上式为何等于cosπ/11cos2π/11cos4π/11cos8π/11cos16π/11**

2022-10-06 14:08:00 14次反馈错误加入收藏正确率 : 100%

题目内容：

cosπ/11cos2π/11cos3π/11cos4π/11cos5π/11
上式为何等于cosπ/11cos2π/11cos4π/11cos8π/11cos16π/11

优质答案解析

王老师

回答题目：2621条

cos3π/11=cos(π-8π/11)=-cos8π/11; cos5π/11=-cos(π+5π/11)=-cos16π/11,
所以cosπ/11*cos2π/11*cos3π/11*cos4π/11*cos5π/11
=cosπ/11*cos2π/11*cos4π/11*cos8π/11*cos16π/11 =2sinπ/11*cosπ/11*cos2π/11*cos4π/11*cos8π/11*cos16π/11]/2sinπ/11
=sin2pai/11*cos2π/11*cos4π/11*cos8π/11*cos16π/11]/2sinπ/11
=sin4pai/11*cos4π/11*cos8π/11*cos16π/11]/4sinπ/11
=sin8pai/11*cos8π/11*cos16π/11]/8sinπ/11
=sin16pai/11*cos16π/11]/16sinπ/11=sin32pai/11]/32sinπ/11=sin10pai/11]/32sinπ/11=1/32

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首页 > 中学数学试题 > 题目详情

**cosπ/11cos2π/11cos3π/11cos4π/11cos5π/11上式为何等于cosπ/11cos2π/11cos4π/11cos8π/11cos16π/11**

题目内容：

cosπ/11cos2π/11cos3π/11cos4π/11cos5π/11
上式为何等于cosπ/11cos2π/11cos4π/11cos8π/11cos16π/11

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