a) \(\eqalign{& {{3\cot g60^\circ } \over {2{{\cos }^2}30^\circ - 1}} \cr & = {{\sqrt 3 } \over {2{{\left( {{{\sqrt 3 } \over 2}} \right)}^2} - 1}} \cr & = {{\sqrt 3 } \over {\displaystyle{3 \over 2} - 1}} = 2\sqrt 3 \cr} \)
b) \(\displaystyle {{\cos 60^\circ } \over {1 + \sin 60^\circ }} + {1 \over {tg30^\circ }} \) \(\displaystyle = {\displaystyle {{1 \over 2}} \over {1 + \displaystyle {{\sqrt 3 } \over 2}}} + \sqrt 3 \) \(\displaystyle = {1 \over {2 + \sqrt 3 }} + \sqrt 3 \) \(\displaystyle = {{2(2 + \sqrt {3)} } \over {2 + \sqrt 3 }} = 2. \)
