Trigonometric system of equations
Source: Poland Math Olympiad 1992 First Round #2
June 2, 2023
algebrasystem of equations
Problem Statement
Given is a natural number . Solve the system of equations:
$
\begin{cases}
\tan (x_1) + 3 \cot (x_1) &= 2 \tan (x_2) \\
\tan (x_2) + 3 \cot (x_2) &= 2 \tan (x_3) \\
& \dots \\
\tan (x_n) + 3 \cot (x_n) &= 2 \tan (x_1) \\
\end{cases}
$