Suppose that $(x_n)$ and $(y_n)$ are sequences and $x_n^2+y_n^2=1$ for all $n\in \mathbb{N}$ .Show that there are positive integers $n_1,n_2,n_3,...$ with $n_1<n_2<n_3...$ such that both $(x_{n_k})$ and $(y_{n_k})$ are converges
how to prove from all sides i am stuck