# 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 $p+q$.

×

Problem Loading...

Note Loading...

Set Loading...