MathDB

18

Part of 1966 IMO Longlists

Problems(1)

Hungary 1

Source: IMO LongList 1959-1966 Problem 18

9/1/2004
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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