你的题目写错了 应该是
cos2π/9*cos4π/9*cos8π/9
原式=(2sin2π/9*cos2π/9*cos4π/9*cos8π/9)/(2sin2π/9)
(即分母分子同乘以2sin2π/9)
=(2sin4π/9*cos4π/9*cos8π/9)/(4sin2π/9)
(合角公式)
=(2sin8π/9*cos8π/9)/(8sin2π/9)
=(sin16π/9)/(8sin2π/9)
=(-sin2π/9)/(8sin2π/9)
=-1/8