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TrigonometrySuperchallengeSum, Difference, and Multiple-Angle Formulas

Sum, Difference, and Multiple-Angle Formulas · Superchallenge problem

An angle xx with 0<x<π20 < x < \dfrac{\pi}{2} satisfies cos⁡x−sin⁡x=12\cos x - \sin x = \dfrac{1}{2}. Find the exact value of sin⁡4x\sin 4x.