IMO Shortlist 1966 problem 50


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2. travnja 2012.
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Solve the equation \frac{1}{\sin x}+\frac{1}{\cos x}=\frac 1p where p is a real parameter.
Discuss for which values of p the equation has at least one real solution and determine the number of solutions in [0, 2\pi) for a given p.
Izvor: Međunarodna matematička olimpijada, shortlist 1966