MathDB
\prod \tan \pi/3 (1+3^k/(3^n-1)]=\prod \cot pi/3 ]1- 3^k/(3^n-1)]

Source: Austrian Polish 1982 APMC

April 30, 2020
Producttrigonometryalgebra

Problem Statement

If n≥2n \ge 2 is an integer, prove the equality ∏k=1ntan⁡π3(1+3k3n−1)=∏k=1ncot⁡π3(1−3k3n−1)\prod_{k=1}^n \tan \frac{\pi}{3}\left(1+\frac{3^k}{3^n-1}\right)=\prod_{k=1}^n \cot \frac{\pi}{3}\left(1-\frac{3^k}{3^n-1}\right)
Back to ProblemsView on AoPS