A Tangent Maximum Under Constraints

★ 8/10trigonometry Extrema Cauchy-Schwarz

Problem

Given

\cos 2\alpha + \cos 2\beta + \cos 2\gamma = 1, \qquad \sin\alpha + \sin\beta + \sin\gamma = 0,

find the maximum value of $\tan\gamma$ .

Answer

Solution

Difficulty	8/10
Topics	trigonometry, Extrema, Cauchy-Schwarz

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