作业帮急 、COSπ/9*COS2π/9*COS4π/9=?同样,
来源：学生作业帮助网 编辑：作业帮 时间：2024/07/17 09:37:58
x){ְTqC}K- mcO'<[]&Hv6128Ȃ * 0P gEPFZ@ nyV) Va# Q<;m +OYaIO[<
84@N1
4&]]>T TП &XDXl \A
急 、COSπ/9*COS2π/9*COS4π/9=?同样,
急 、COSπ/9*COS2π/9*COS4π/9=?同样,
急 、COSπ/9*COS2π/9*COS4π/9=?同样,
π/9=20°2π/9=40°4π/9=80°
cos20cos40cos80
=sin20cos20cos40cos80/sin20
=1/2*sin40cos40cos80/sin20
=1/4*sin80cos80/sin20
=1/8*sin160/sin20
=1/8*sin20/sin20
=1/8
利用2倍角公式
cosπ/9*cos2π/9*cos4π/9
=[sinπ/9*cosπ/9*cos2π/9*cos4π/9]/sinπ/9
=[1/2sin2π/9*cos2π/9*cos4π/9]/sinπ/9
=[1/4sin4π/9*cos4π/9]/sinπ/9
=[1/8sin8π/9]/sinπ/9
=[1/8sinπ/9]/[sinπ/9]
=1/8