1. It is known that $\sin x=2 \cos y-\frac{5}{2} \sin y, \cos x=2 \sin y-\frac{5}{2} \cos y$. Find $\sin 2 y$.
Answer. $\sin 2 y=\frac{37}{40}$.

Solution. Squaring both equalities and adding them term by term, we get $1=4-20 \sin y \cos y+\frac{25}{4}$, from which $10 \sin 2 y=\frac{37}{4}, \sin 2 y=\frac{37}{40}$.