# The sines speak otherwise...

Geometry Level 3

Given that $$\frac{\sin x}{\sin y} = 3$$ and $$\frac{\cos x}{\cos y} = \frac{1}{2}$$, the value of $$\frac{\sin2x}{\sin2y}- \frac{\cos2x}{\cos2y}$$ can be expressed as $$\frac{p}{q}$$ for positive coprime integers $$p$$ and $$q$$. Find $$p+q$$.

Note: This is a modified AIME problem.

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