搜搜做题作业网数学题求解.兀/7的余弦+ 3兀/7的余弦+ 5兀/7的余弦=1/2
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数学题求解.兀/7的余弦+ 3兀/7的余弦+ 5兀/7的余弦=1/2
积化和差公式:
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) 括号里用积化和差
=sin6π/7/(2sinπ/7)
=sin(π-π/7)/(2sinπ/7)
=sinπ/7/(2sinπ/7)
=1/2
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) 括号里用积化和差
=sin6π/7/(2sinπ/7)
=sin(π-π/7)/(2sinπ/7)
=sinπ/7/(2sinπ/7)
=1/2