Question

Evaluate the following.
$\frac{\cos {45}^o}{\sec {30}^o+\csc {60}^o}$

Answer 1

$\frac{\cos {45}^o}{\sec {30}^o+cosec{60}^o}=\frac{1/\sqrt{2}}{2/\sqrt{3}+2/\sqrt{3}}$

$\Rightarrow \frac{1/\sqrt{2}}{4/\sqrt{3}}$

$\Rightarrow \frac{\sqrt{3}}{4\sqrt{2}}$.