Question

Solve $\frac{\cos {45}^o}{(\sec {30}^o+\csc {30}^o)}$

Answer 1

$\frac{\cos {45}^o}{\left(\sec {30}^o+\csc {30}^o\right)}$

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

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

$=\frac{\sqrt{6}\left(\sqrt{-}1\right)}{4(3-1)}$

$=\frac{\sqrt{6}\left(\sqrt{-}1\right)}{8}$