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Unsolved Challenge Unsolved Challenge: Σ(cosAcosB)>√(cosAcosBcosC)

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,599
Let $ABC$ be a non-obtuse triangle. Prove that $\cos A \cos B+\cos B \cos C+\cos C \cos A>2\sqrt{\cos A \cos B \cos C}$.