System of trigonometric equations
Source: Czech and Slovak Olympiad 1959, National Round, Problem 4
June 14, 2024
system of equationstrigonometry
Problem Statement
Find all pair in degrees such that
\begin{align*}
&\sin (x + 150^\circ) = \cos (y - 75^\circ), \\
&\cos x + \sin (y - 225^\circ) + \frac{\sqrt3}{2} = 0.
\end{align*}