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Solve the equation for a real parameter p

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September 27, 2010
parameterizationtrigonometryparabolaTrigonometric EquationsIMO ShortlistIMO Longlist

Problem Statement

Solve the equation 1sin⁡x+1cos⁡x=1p\frac{1}{\sin x}+\frac{1}{\cos x}=\frac 1p where pp is a real parameter. Discuss for which values of pp the equation has at least one real solution and determine the number of solutions in [0,2π)[0, 2\pi) for a given p.p.
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