Question

$\frac{2\cos {40}^o-\cos {20}^o}{\sin {20}^o}$.

Answer 1

$\begin{array}{cc}\frac{2\cos 40-\cos 20}{\sin 20}=\frac{\cos 40+\cos 40-\cos 20}{\sin 20}& \\ =\frac{\cos 40+2\sin 20\sin 10}{\sin 20}=\frac{\cos 40}{\sin 20}2\times \frac{1}{2}\sin 10& \\ =\sin \frac{50+\sin 10}{\sin 20}=\frac{2\cos 30\sin 20}{\sin 20}& \\ \sin 50=\cos 40& =2\times \frac{\sqrt{3}}{2}=\sqrt{3}\end{array}$