This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 2

1996 Tuymaada Olympiad, 6
Tags: limit , algebra , sequence , limit of sequence , trigonometric
Given the sequence $f_1(a)=sin(0,5\pi a)$ $f_2(a)=sin(0,5\pi (sin(0,5\pi a)))$ $...$ $f_n(a)=sin(0,5\pi (sin(...(sin(0,5\pi a))...)))$ , where $a$ is any real number. What limit aspire the members of this sequence as $n \to \infty$?

2010 Sharygin Geometry Olympiad, 2
Tags: circles , geometry , trigonometry , trigonometric , circumcircle
Each of two equal circles $\omega_1$ and $\omega_2$ passes through the center of the other one. Triangle $ABC$ is inscribed into $\omega_1$, and lines $AC, BC$ touch $\omega_2$ . Prove that $cosA + cosB = 1$.