Inspired by Shivamani Patil
Geometry
Level
4
\[\Large \dfrac{\tan(x + 120^{\circ})}{\tan(x - 30^{\circ})} = \dfrac{11}{2}\]
If \(x\) is a solution to the above equation, and \(\cos(4x) = \dfrac{a}{b},\) where \(a\) and \(b\) are positive coprime integers, then find \(a + b.\)
by
Brian Charlesworth