n-2-Prove-that-k-1-n-tg-pi-3-1-3-k-3-n-1-k-1-n-ctg-pi-3-1-3-k-3-n-1-

Question Number 217871 by hardmath last updated on 22/Mar/25

n ⩾ 2

Prove that :

\underset{k = 1}{\prod^{n}} tg [\frac{π}{3} (1 + \frac{3^{k}}{3^{n} - 1})] = \underset{k = 1}{\prod^{n}} ctg [\frac{π}{3} (1 - \frac{3^{k}}{3^{n} - 1})]