Question

求值cos2π/9*cos4π/9*8π/9

Answer 1

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