$\cos ec{15}^o+\sec {15}^o$ is equal to

$\cos ec{15}^o+\sec {15}^o$$=\frac{2\left(\sin {15}^o+\cos {15}^o\right)}{2\sin {15}^o\cos {15}^o}$

$\frac{2\left(\begin{array}{l}\sin {45}^o\cos {30}^o-\cos {45}^o\sin {30}^o\\ +\cos {45}^o\cos {30}^o+\sin {45}^o\sin {30}^o\end{array}\right)}{\sin {30}^o}$

$=4\left[\frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}+\frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2\sqrt{2}}\right]$

$=4\left[\frac{2\sqrt{3}}{2\sqrt{2}}\right]=2\sqrt{6}$