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Parametric trigonometric equation

Source: 2007 Bulgarian Autumn Math Competition, Problem 12.1

March 17, 2022
algebraTrigonometric Equationsparameterparameterization

Problem Statement

Determine the values of the real parameter aa, such that the equation sin⁡2xsin⁡4x−sin⁡xsin⁡3x=a\sin 2x\sin 4x-\sin x\sin 3x=a has a unique solution in the interval [0,π)[0,\pi).
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