Question

Evaluate :
$(3-\cot {30}^{\circ })-{\tan }^3{60}^{\circ }+2\tan {60}^{\circ }$

Answer 1

We know that $\cot {30}^{\circ }=\sqrt{3},\tan {60}^{\circ }=\sqrt{3}$

$3-\cot {30}^{\circ }-{\tan }^3{60}^{\circ }+2\tan {60}^{\circ }$

$=3-\sqrt{3}-{\left(\sqrt{3}\right)}^3+2\sqrt{3}$

$=3-\sqrt{3}-3\sqrt{3}+2\sqrt{3}$

$=3-2\sqrt{3}$