$\dfrac{\cos60^o}{1 + \sin60^o} + \dfrac{1}{\cot60^o}$
$=\dfrac{\cos60^o}{1 + \sin60^o} + \dfrac{\sin60^o}{\cos60^o}$
$= \dfrac{\cos^260^o + \sin60^o(1 + \sin60^o)}{(1 + \sin60^o)\cos60^o}$
$= \dfrac{1 + \sin60^o}{(1 + \sin60^o)\cos60^o}$
$= \dfrac{1}{\cos60^o} = \dfrac{1}{\dfrac{1}{2}} = 2$