Скачать или смотреть Advanced Trigonometry Problem Solved: CMO 2024 - Finding cos C Using Trig Identities!

Join me as we solve a fascinating trigonometry problem from the China Math Olympiad 2024. In this problem, we are given the equation
\cos C = \frac{\sin A + \cos A}{2} = \frac{\sin B + \cos B}{2}
and tasked with finding \cos C .

The key trick involves recognizing that
\sin A + \cos A = \sqrt{2} \sin(A + \frac{\pi}{4}) .

I’ll guide you through the algebraic manipulations and trigonometric identities needed to solve this challenging problem step by step. Perfect for students preparing for advanced math competitions!

This description highlights the key insight of the problem and the advanced methods used, while the title captures the complexity and intrigue of the solution.

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