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Trigonometric System

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April 6, 2013
trigonometryAMCAMC 12

Problem Statement

Let aa and bb be real numbers such that sin⁡a+sin⁡b=22\sin a+\sin b=\dfrac{\sqrt2}2 and cos⁡a+cos⁡b=62\cos a+\cos b=\dfrac{\sqrt6}2. Find sin⁡(a+b)\sin(a+b).
<spanclass=′latex−bold′>(A)</span>12<spanclass=′latex−bold′>(B)</span>22<spanclass=′latex−bold′>(C)</span>32<spanclass=′latex−bold′>(D)</span>62<spanclass=′latex−bold′>(E)</span>1<span class='latex-bold'>(A) </span>\dfrac12\qquad<span class='latex-bold'>(B) </span>\dfrac{\sqrt2}2\qquad<span class='latex-bold'>(C) </span>\dfrac{\sqrt3}2\qquad<span class='latex-bold'>(D) </span>\dfrac{\sqrt6}2\qquad<span class='latex-bold'>(E) </span>1
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