Question

Find the value of: $\frac{\sin {30}^0}{1+\cos {30}^0}+\frac{1+\cos {30}^0}{\sin {30}^0}$

Answer 1

$\begin{array}{c}Wehave\\ \frac{\sin {30}^{\circ }}{1+\cos {30}^{\circ }}+\frac{1+\cos {30}^{\circ }}{\sin {30}^{\circ }}\\ =\frac{\frac{1}{2}}{1+\frac{\sqrt{3}}{2}}+\frac{1+\frac{\sqrt{3}}{2}}{\frac{1}{2}}\left[onputtingthevalueof\sin {30}^{\circ }and\cos {30}^{\circ }\right]\end{array}$

$=\frac{1}{2+\sqrt{3}}+2+\sqrt{3}$

$=\frac{1+(2+\sqrt{3}{)}^2}{2+\sqrt{3}}$

Hence, this is the answer.