求值cos2π/9*cos4π/9*8π/9
问题描述：
求值cos2π/9*cos4π/9*8π/9
答
上下乘 sin2π/9
原式=sin2π/9cos2π/9*cos4π/9*8π/9/sin2π/9
=1/2*sin4π/9*cos4π/9*8π/9/sin2π/9
=1/4*sin8π/9*8π/9/sin2π/9
=1/8*sin16π/9/sin2π/9
=(1/8)*sin(2π-2π/9)/sin2π/9
=(1/8)*(-sin2π/9)/sin2π/9
=-1/8
答
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