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2020 Taiwan APMO Preliminary Problem 1

Source: 2020 Taiwan APMO Preliminary

July 23, 2020
Taiwanalgebratrigonometry

Problem Statement

Let △ABC\triangle ABC satisfies cos⁡A:cos⁡B:cos⁡C=1:1:2\cos A:\cos B:\cos C=1:1:2, then sin⁡A=t\sin A=\sqrt{t}(s∈N,t∈Q+s\in\mathbb{N},t\in\mathbb{Q^+} and tt is an irreducible fraction). Find s+ts+t.
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