IMO Shortlist 1969 problem 29


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2. travnja 2012.
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(GDR 1) Find all real numbers \lambda such that the equation \sin^4 x - \cos^4 x = \lambda(\tan^4 x - \cot^4 x)
(a) has no solution,
(b) has exactly one solution,
(c) has exactly two solutions,
(d) has more than two solutions (in the interval (0, \frac{\pi}{4}).
Izvor: Međunarodna matematička olimpijada, shortlist 1969