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MathNet 2008-part-03 — 165 problems (EN–VI) Question 73

Math Olympiad Vault · MathNet 2008-part-03 — 165 problems (EN–VI)

Question 73

Prove that there is an angle $x$ such that
$$
\sin x = \frac{\sin \beta \cdot \sin \gamma}{1 - \cos \alpha \cdot \cos \beta \cdot \cos \gamma},
$$
for every angle $\alpha$, and $\beta$ and $\gamma$ acute angles.