Trigonometeric Function

4\cos\left(20\right)-\sqrt{3}\cot\left(20 \right) \\ \\ \frac{2\sin(40)-\sqrt{3}\cos (20)}{\sin (20)} \\ \frac{2}{\sin(20)}*(\sin(60-20)-\frac{\sqrt{3}}{2}\cos (20)) \\ \frac{2}{\sin(20)}*(-\frac{\sin (20)}{2})= \boxed{-1}

\frac{2\cos(40)-\cos(20)}{\sin(20)} \\ \frac{2}{\sin(20)}*(\cos(60-20)-\cos(20)) \\ \texttt{Now,expand using cos(A-B) formula }\\ \boxed{Ans.=\sqrt{3}}