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2012 AIME II Problems/Problem 9

Revision as of 15:09, 31 March 2012 by Williamhu888 (talk | contribs) (Created page with "== Problem 9 == Let <math>x</math> and <math>y</math> be real numbers such that <math>\frac{\sin x}{\sin y} = 3</math> and <math>\frac{\cos x}{\cos y} = \frac12</math>. The value...")
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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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