Using sum or difference formulas, find the exact value of $\cos(105^{\circ})$. Express your answer in the form $\displaystyle \cos(105^{\circ}) = \frac{ \sqrt{a} ( 1 - \sqrt{b} ) }{ 4 }$ for some numbers $a$ and $b$.

$a =$ help (numbers)
$b =$ help (numbers)

Hint: