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TrigonometryChallengeSum, Difference, and Multiple-Angle Formulas

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

For every real xx, the expression cos⁡2x+cos⁡2(x+30∘)−2cos⁡xcos⁡30∘cos⁡(x+30∘)\cos^2 x + \cos^2(x + 30^\circ) - 2\cos x\cos 30^\circ\cos(x + 30^\circ) has the same value. Find it.