作业帮 > 综合 > 作业

求数学高手帮忙cos(2π/7)+cos(4π/7))+cos(6π/7)=?(化简求值)

来源:学生作业帮 编辑:作业帮 分类:综合作业 时间:2024/05/25 11:40:31
求数学高手帮忙cos(2π/7)+cos(4π/7))+cos(6π/7)=?(化简求值)
cos(2π/7)+cos(4π/7)+cos(6π/7)
=[sin(2π/7)cos(2π/7)+sin(2π/7)cos(4π/7)+sin(2π/7)cos(6π/7)]/sin(2π/7)
(下面用积化和差)
=1/2[sin(4π/7)+sin(6π/7)-sin(2π/7)+sin(8π/7)-sin(4π/7)]/sin(2π/7)
=1/2[sin(6π/7)-sin(2π/7)+sin(8π/7)]/sin(2π/7)
=1/2[-sin(2π/7)]/sin(2π/7)
=-1/2