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P07 [Algebra] - Turkish NMO 1st Round - 2005

Source:

November 2, 2013
trigonometryinequalitiesrearrangement inequality

Problem Statement

What is the greatest value of sin⁡xcos⁡y+sin⁡ycos⁡z+sin⁡zcos⁡x\sin x \cos y + \sin y \cos z + \sin z \cos x, where x,y,zx,y,z are real numbers?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 32<spanclass=′latex−bold′>(C)</span> 32<spanclass=′latex−bold′>(D)</span> 2<spanclass=′latex−bold′>(E)</span> 3 <span class='latex-bold'>(A)</span>\ \sqrt 2 \qquad<span class='latex-bold'>(B)</span>\ \dfrac 32 \qquad<span class='latex-bold'>(C)</span>\ \dfrac {\sqrt 3}2 \qquad<span class='latex-bold'>(D)</span>\ 2 \qquad<span class='latex-bold'>(E)</span>\ 3
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