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5:37 AM
Maybe someone will notice this here and will be able to help:
in Calculus and real analysis, 1 min ago, by Sawarnik
@MartinSleziak Do you know of any quantities related to $\cos \left(\frac{B-C}{2}\right) + \cos \left(\frac{C-A}{2}\right) + \cos \left(\frac{A-B}{2}\right)$ in a triangle. Or where could I hope to find them?
@Sawarnik I am not sure if this will be of any help, but there was similar question on the main, but without 2 in denominator.
The book Inequalities: A Mathematical Olympiad Approach has a chapter on geometric inequalities. Maybe this would be one possible place where to look for similar problems.
 

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