A Tangent Maximum From a Cosine

★ 7/10trigonometry Trigonometric Identities AM-GM

Problem

Acute angles $\alpha, \beta$ satisfy

\cos(\alpha + \beta) = \frac{\sin\alpha}{\sin\beta}.

Find the maximum of $\tan\alpha$ .

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Trigonometric Identities, AM-GM

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