求cosπ/9*cos2π/9*cos4π/9的值如题

求cosπ/9*cos2π/9*cos4π/9的值如题
求cosπ/9*cos2π/9*cos4π/9的值
如题

求cosπ/9*cos2π/9*cos4π/9的值如题
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

cosπ/9*cos2π/9*cos4π/9
=2sinπ/9*cosπ/9*cos2π/9*cos4π/9/(2sinπ/9)
=sin2π/9*cos2π/9*cos4π/9/(2sinπ/9)
=2sin2π/9*cos2π/9*cos4π/9/(4sinπ/9)
=sin4π/9*cos4π/9/(4sinπ/9)
=2sin4π/9*cos4π/9/(8sinπ/9)
=sin8π/9/(8sinπ/9)
=sin(π-π/9)/(8sinπ/9)
=sinπ/9/(8sinπ/9)
=1/8

(sinπ/9*cosπ/9*cos2π/9*cos4π/9)/(sinπ/9)=(sin8π/9)/8(sinπ/9)
=(sinπ/9)/8(sinπ/9)=1/8