Parametrized system of trigonometric equations
Source: Czech and Slovak Olympiad 1978, National Round, Problem 3
October 11, 2024
algebratrigonometrysystem of equationsangles
Problem Statement
Let be angles of a triangle. Determine all real triplets satisfying the system
\begin{align*}
x\cos\beta+\frac1z\cos\alpha &=1, \\
y\cos\gamma+\frac1x\cos\beta &=1, \\
z\cos\alpha+\frac1y\cos\gamma &=1.
\end{align*}