cosπ/9*cos2π/9*cos4π/9怎么算的?

cosπ/9*cos2π/9*cos4π/9怎么算的?
cosπ/9*cos2π/9*cos4π/9怎么算的?

cosπ/9*cos2π/9*cos4π/9怎么算的?
分子分母同乘以8sin(π/9),然后分子连续使用二倍角公式====>>>> 2sinacosa=sin2a
===>>>>> 原式=[sin(8π/9)]/[8sin(π/9)]=1/8

上下乘16sinπ/9sin2π/9sin3π/9sin4π/9 原式=(2sinπ/9cosπ/9)(2sin2π/9cos2π/9)(2sin3π/9cos3π/9)(2sin4π/9cos4π/9)/(1616