2012 AIME II Problems/Problem 9

Problem 9

Let $x$ and $y$ be real numbers such that $\frac{\sin x}{\sin y} = 3$ and $\frac{\cos x}{\cos y} = \frac12$ . The value of $\frac{\sin 2x}{\sin 2y} + \frac{\cos 2x}{\cos 2y}$ can be expressed in the form $\frac pq$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ .

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2012 AIME II (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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2012 AIME II Problems/Problem 9

Problem 9

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