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Evaluate : $\frac{\cos 45^\circ}{\sec 30^\circ + \csc 30^\circ}$
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Solution: $\frac{\cos 45^\circ}{\sec 30^\circ + \csc 30^\circ} = \frac{\frac{1}{\sqrt{2}}}{\frac{2}{\sqrt{3}} + 2}$ [1 1/2 marks]
$= \frac{\sqrt{3}}{2\sqrt{2} + 2\sqrt{6}}$ or $\frac{3\sqrt{2} - \sqrt{6}}{8}$ [1/2 mark]
$= \frac{\sqrt{3}}{2\sqrt{2} + 2\sqrt{6}}$ or $\frac{3\sqrt{2} - \sqrt{6}}{8}$ [1/2 mark]