Evaluate : $\displaystyle \frac{\cos 45^{\circ}+\sin 60^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}}$.

\[\begin{aligned} & \frac{\cos 45^{\circ}+\sin 60^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}} \\ & =\frac{\dfrac{1}{\sqrt{2}}+\dfrac{\sqrt{3}}{2}}{\dfrac{2}{\sqrt{3}}+2} \\ & =\frac{2 \sqrt{3}+3 \sqrt{2}}{4 \sqrt{2}(1+\sqrt{3})} \end{aligned} \]