Question

Evaluate the following.
$\frac{\cos {45}^o}{\sec {30}^o+\text{cosec}{30}^o}$.

Answer 1

$\frac{\cos {45}^{\circ }}{\sec {30}^{\circ }+cosec{30}^{\circ }}$

$=\frac{\frac{1}{\sqrt{2}}}{\frac{1}{\cos {30}^{\circ }}+\frac{1}{\sin {30}^{\circ }}}$

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

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

$=\frac{\sqrt{3}}{2\sqrt{2}+2\sqrt{6}}$