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Evaluate: $\frac{2 \sin^2 60^\circ + \cos^2 60^\circ}{\tan^2 30^\circ}$
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Solution: (b) $\frac{2 \sin^2 60^\circ + \cos^2 60^\circ}{\tan^2 30^\circ}$
$= \frac{2 \left( \frac{\sqrt{3}}{2} \right)^2 + \left( \frac{1}{2} \right)^2}{\left( \frac{1}{\sqrt{3}} \right)^2}$ (3$\times$1/2 Mark)
$= \frac{21}{4}$ (1/2 Mark)
$= \frac{2 \left( \frac{\sqrt{3}}{2} \right)^2 + \left( \frac{1}{2} \right)^2}{\left( \frac{1}{\sqrt{3}} \right)^2}$ (3$\times$1/2 Mark)
$= \frac{21}{4}$ (1/2 Mark)