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Trigonometric inequality

Source: IMOTC 2015 Practice Test 1 Problem 3

July 11, 2015
trigonometryinequalities

Problem Statement

Prove that for any triangle ABCABC, the inequality ∑cycliccos⁡A≤∑cyclicsin⁡(A/2)\displaystyle\sum_{\text{cyclic}}\cos A\le\sum_{\text{cyclic}}\sin (A/2) holds.
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