2012 AIME II 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.