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Evaluate $\frac{5 \cos^2 60^\circ + 4 \sec^2 30^\circ – \tan^2 45^\circ}{\sin^2 30^\circ + \cos^2 30^\circ}$
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Sol. $\frac{5 \cos^2 60^\circ + 4 \sec^2 30^\circ - \tan^2 45^\circ}{\sin^2 30^\circ + \cos^2 30^\circ} = \frac{5(1/2)^2 + 4(2/\sqrt{3})^2 - (1)^2}{1}$
$= \frac{5/4 + 16/3-1}{1} = \frac{67}{12}$
$= \frac{5/4 + 16/3-1}{1} = \frac{67}{12}$