Question

Find the value of $\frac{\cos {30}^o\tan {60}^o+\sin {60}^o\cot {60}^o}{\csc {30}^o\sec {60}^o-\csc {60}^o\cot {30}^o}$

Answer 1

$\begin{array}{c}\Rightarrow \left[\frac{\frac{\sqrt{3}}{2}\cdot \sqrt{3}+\frac{\sqrt{3}}{2}\cdot \frac{1}{\sqrt{3}}}{2\cdot 2-\frac{2}{\sqrt{3}}\cdot \sqrt{3}}\right]\\ \Rightarrow \frac{\left(\frac{3}{2}+\frac{1}{2}\right)}{\left(4-2\right)}=\frac{\frac{4}{2}}{2}=1\end{array}$