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Finding real numbers lambda

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September 29, 2010
trigonometryalgebraTrigonometric EquationsIMO ShortlistIMO Longlist

Problem Statement

(GDR1)(GDR 1) Find all real numbers λ\lambda such that the equation sin⁡4x−cos⁡4x=λ(tan⁡4x−cot⁡4x)\sin^4 x - \cos^4 x = \lambda(\tan^4 x - \cot^4 x) (a)(a) has no solution, (b)(b) has exactly one solution, (c)(c) has exactly two solutions, (d)(d) has more than two solutions (in the interval (0,π4).(0, \frac{\pi}{4}).
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