Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.3 AIME, harder Prove it Philippines

Problem:
If $0 < \theta < \pi / 2$ and $1 + \sin \theta = 2 \cos \theta$ , determine the numerical value of $\sin \theta$ .

Solution

Solution:
$\frac{3}{5}$

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.