求值cosπ⼀7+cos2π⼀7+cos3π⼀7+cos4π⼀7+cos5π⼀7+cos6π⼀7=?

2025-01-07 15:49:46
推荐回答(2个)
回答1:

答案是0啊,从前面开始每两项加起来得0

回答2:

cosπ/7+cos2π/7+cos3π/7+cos4π/7+cos5π/7+cos6π/7=(cosπ/7+cos2π/7+cos3π/7+cos4π/7+cos5π/7+cos6π/7)*cosπ/7/cosπ/7=(cosπ/7cosπ/7+cos2π/7cosπ/7+cos3π/7cosπ/7+cos4π/7cosπ/7+cos5π/7cosπ/7+cos6π/7cosπ/7)/cosπ/7=(1-cos2π/7+cosπ/7-cos3π/7+cos2π/7-cos4π/7+cos3π/7-cos5π/7+cos4π/7-cos6π/7+cos5π/7-cosπ)/(2cosπ/7)=(1+cosπ/7-cos6π/7-cosπ)/(2cosπ/7)=(2+2cosπ/7)/(2cosπ/7)=1/cosπ/7 +1