cosπ/7-cos2π/7+cos3π/7
答案:1 悬赏:0
解决时间 2021-01-14 02:59
- 提问者网友：城市野鹿
- 2021-01-13 22:37
cosπ/7-cos2π/7+cos3π/7
最佳答案
- 二级知识专家网友：行雁书
- 2021-01-14 00:10
cosπ/7-cos2π/7+cos3π/7
=cosπ/7+cos3π/7+cos5π/7
=(2sinπ/7*cosπ/7+2sinπ/7*cos3π/7+2sinπ/7*cos5π/7)/(2sinπ/7)
=[sin2π/7+(sin4π/7-sin2π/7)+(sin6π/7-sin4π/7)]/(2sinπ/7)
=(sin6π/7)/(2sinπ/7)
=(sinπ/7)/(2sin/π7)
=1/2
=cosπ/7+cos3π/7+cos5π/7
=(2sinπ/7*cosπ/7+2sinπ/7*cos3π/7+2sinπ/7*cos5π/7)/(2sinπ/7)
=[sin2π/7+(sin4π/7-sin2π/7)+(sin6π/7-sin4π/7)]/(2sinπ/7)
=(sin6π/7)/(2sinπ/7)
=(sinπ/7)/(2sin/π7)
=1/2
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