2
$\begingroup$

Let $A, B, C$ be angles in a triangle. Is the following inequality $$4\cos A \le 1 + \cos\left(\frac{B-C}{2}\right)$$ true? I just assume it but don't have a proof. Thank you for your help.

  • 0
    Thank you N.S. This was very stupid attempt to prove the true inequality $$4(\cos A + \cos B + \cos C) \le 3 + \cos(\frac{B-C}{2}) + \cos(\frac{C-A}{2}) + \cos(\frac{A-B}{2}).$$ Any idea how this can be done?2012-07-23

1 Answers 1