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Hungary 1

Source: IMO LongList 1959-1966 Problem 18

September 1, 2004
trigonometryalgebra proposedalgebra

Problem Statement

Solve the equation 1sin⁡x+1cos⁡x=1p,\frac{1}{\sin x}+\frac{1}{\cos x}=\frac{1}{p}, where pp is a real parameter. Investigate for which values of pp solutions exist and how many solutions exist.
(Of course, the last question ''how many solutions exist'' should be understood as ''how many solutions exists modulo 2π2\pi ''.)
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