# Trigonometric Arithmetic III

Geometry Level 3

$\sec ^{ 2 }{ x } -\left (\cos { x } +\sin { x } \tan { \frac { x }{ 2 } } \right )=\frac { \sin {(x-30^\circ)} +\cos{(60^\circ-x)} }{ \cos{x} }$

If the solution for the trigonometric equation above is $$x=a^\circ(bn+1)$$, for integers $$a,b,n$$ and $$a,b > 0$$, what is the value of $$\dfrac a b$$?

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