# System of equations

Geometry Level 4

Given that $$\dfrac{\sin x}{\sin y}=4$$ and $$\dfrac{\cos x}{\cos y}=\dfrac{1}{3}$$.

And if $$\dfrac{\sin 2x}{\sin 2y}+\dfrac{\cos 2x}{\cos 2y}=\dfrac{m}{n}$$, where $$m,n$$ are co-prime positive integers, find the value of $$m+n$$.

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