# Working with Tangents

Geometry Level 5

$\large \dfrac { \sin x }{ \cos y } +\dfrac { \sin y }{ \cos x } =1, \ \ \ \ \ \dfrac { \cos x }{ \sin y } +\dfrac { \cos y }{ \sin x } =6$

Let $$x,y$$ be real numbers that satisfy the equations above.

Suppose that $$\dfrac { \tan x }{ \tan y } +\dfrac { \tan y }{ \tan x } =\dfrac{p}{q}$$ for relatively prime positive integers $$p$$ and $$q$$. Find $$p+q$$.

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