Evaluate each of the following: 4/cot^2 30° + 1/cot^2 60° - cos^2 45°

Question

Evaluate each of the following:

\(\frac{4}{cot^230°}\) + \(\frac{1}{cot^260°}\) - cos² 45°

Answer 1

 \(\frac{4}{cot^230°}\) + \(\frac{1}{cot^260°}\) - cos² 45° = \(\frac{4}{(\sqrt3)^2}\) + \(\frac{1}{(\frac{\sqrt3}{2})^2}\) - \((\frac{1}{\sqrt2})^2\)

= \(\frac{4}3\) + \(\frac{4}3\) - \(\frac{1}2\) = \(\frac{13}6\)