50
Evaluate: $\frac{\cos 45^\circ + \sin 60^\circ}{\sec 30^\circ + \operatorname{cosec} 30^\circ}$
Show SolutionHide Solution↓
$\frac{\cos 45^\circ + \sin 60^\circ}{\sec 30^\circ + \operatorname{cosec} 30^\circ}$
$= \frac{\frac{1}{\sqrt{2}} + \frac{\sqrt{3}}{2}}{\frac{2}{\sqrt{3}} + 2}$
$= \frac{2\sqrt{3}+3\sqrt{2}}{4\sqrt{2}(1+\sqrt{3})}$
$= \frac{\frac{1}{\sqrt{2}} + \frac{\sqrt{3}}{2}}{\frac{2}{\sqrt{3}} + 2}$
$= \frac{2\sqrt{3}+3\sqrt{2}}{4\sqrt{2}(1+\sqrt{3})}$