求值:cos 派/7 + cos 3派/7 + cos 5派/7
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求值:cos 派/7 + cos 3派/7 + cos 5派/7
请给出过程(若实在太麻烦,给个思路也行),
请给出过程(若实在太麻烦,给个思路也行),
![求值:cos 派/7 + cos 3派/7 + cos 5派/7](/uploads/image/z/8108097-33-7.jpg?t=%E6%B1%82%E5%80%BC%EF%BC%9Acos+%E6%B4%BE%2F7+%2B+cos+3%E6%B4%BE%2F7+%2B+cos+5%E6%B4%BE%2F7)
cosπ/7+cos3π/7+cos5π/7
=(sinπ/7cosπ/7+sinπ/7cos3π/7+sinπ/7cos5π/7)/sinπ/7
=[sin2π/7+(sin4π/7-sin2π/7)+(sin6π/7-sin4π/7)/(2sinπ/7)
=sin6π/7/(2sinπ/7)
=sin(π-π/7)/(2sinπ/7)
=sinπ/7/(2sinπ/7)
=1/2
=(sinπ/7cosπ/7+sinπ/7cos3π/7+sinπ/7cos5π/7)/sinπ/7
=[sin2π/7+(sin4π/7-sin2π/7)+(sin6π/7-sin4π/7)/(2sinπ/7)
=sin6π/7/(2sinπ/7)
=sin(π-π/7)/(2sinπ/7)
=sinπ/7/(2sinπ/7)
=1/2
求值:cos 派/7 + cos 3派/7 + cos 5派/7
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