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SMO 2023 Open Round 1 Question 11

SMO · SMO 2023 Open Round 1

Question 11

Let $ABC$ be a triangle satisfying the following conditions that $\angle A+\angle C=2\angle B$, and $\dfrac1{\cos A}+\dfrac1{\cos C}=\dfrac{-\sqrt2}{\cos B}$. Determine the value of $\dfrac{2022\cos\left(\frac{A-C}{2}\right)}{\sqrt2}$.