Evaluate: $\frac{5 \cos^2 60° + 4 \sec^2 30° - an^2 45°}{\sin^2 30° + \cos^2 30°}$

Question

Evaluate: $\frac{5 \cos^2 60° + 4 \sec^2 30° - 	an^2 45°}{\sin^2 30° + \cos^2 30°}$

Accepted Answer

Step 1: $= \frac{5\left(\frac{1}{2}\right)^2 + 4\left(\frac{2}{\sqrt{3}}\right)^2 - (1)^2}{\left(\frac{1}{2}\right)^2 + \left(\frac{\sqrt{3}}{2}\right)^2} = \frac{\frac{5}{4} + \frac{16}{3} - 1}{\frac{1}{4} + \frac{3}{4}}$
Step 2: $= \frac{\frac{5}{4} + \frac{16}{3} - 1}{1} = \frac{15 + 64 - 12}{12} = \frac{67}{12}$

Question

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