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

Question

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

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: $= \frac{\frac{15 + 64 - 12}{12}}{1} = \frac{67}{12}$

Question

Solution