一道高一数学题,请高手解答,要详细过程

来源:百度知道 编辑:UC知道 时间:2024/05/31 21:55:17
求值:(cos2π/7)*(cos4π/7)*(cos6π/7)
“π”是派

=-(cos2π/7)*(cos4π/7)*(cosπ/7) *sin(π/7)/sin(π/7)
=-1/2(cos2π/7)*(cos4π/7)*sin(2π/7)/sin(π/7)
=-1/4sin(4π/7)(cos4π/7)/sin(π/7)
=-1/8sin(8π/7)/sin(π/7)
=1/8sin(π/7)/sin(π/7)
=1/8

设M=(cos2π/7)*(cos4π/7)*(cos6π/7)
N=(sin2π/7)*(sin4π/7)*(sin6π/7)
则M* N=(cos2π/7)*(cos4π/7)*(cos6π/7)*(sin2π/7)*(sin4π/7)*(sin6π/7)
=[(cos2π/7)*(sin2π/7)]*[(cos4π/7)*(sin4π/7)]*[(cos6π/7)*(sin6π/7)]
=[(sin4π/7)/2]*[(sin8π/7)/2]*[(sin12π/7)/2]
=[(sin4π/7)]*[sin(2π-8π/7)]*[sin(2π-12π/7)]/8
=(sin2π/7)*(sin4π/7)*(sin6π/7)/8
所以,原式就等于八分之一