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Solve the trigonometric equation

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September 25, 2010
trigonometryalgebraTrigonometric EquationsequationIMO ShortlistIMO Longlist

Problem Statement

Find xx such that trigonometric sin⁡3xcos⁡(60∘−x)+1sin⁡(60∘−7x)−cos⁡(30∘+x)+m=0\frac{\sin 3x \cos (60^\circ -x)+1}{\sin(60^\circ - 7x) - \cos(30^\circ + x) + m}=0 where mm is a fixed real number.
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