A problem from AMC

Posted by Nalin Pithwa

Problem:

Let a and b be real numbers such that

$\sin{a}+\sin{b}=\frac{\sqrt{2}}{2}$

$\cos{a}+\cos{b}=\frac{\sqrt{6}}{2}$ .

Evaluate $\sin {(a+b)}$ .

From AMC12 2002

Happy problem-solving! :-),

Nalin Pithwa

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