MathDB
Sum of cosines of differences

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October 28, 2019
Trigonometric inequalityinequalitiestrigonometry

Problem Statement

Let be a natural number n, n, and n n real numbers a1,a2,…,an. a_1,a_2,\ldots ,a_n . Then, ∑1≤i<j≤ncos⁡(ai−aj)≥−n/2. \sum_{1\le i<j\le n} \cos\left( a_i-a_j \right)\ge -n/2.
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