Evaluate each of the following: sin30°/sin45° + tan 45°/sec 60° - sin 60°/cot 45° - cos 30°/sin 90°

Question

Evaluate each of the following:

\(\frac{sin30°}{sin45°}\) + \(\frac{tan45°}{sec60°}\) - \(\frac{sin60°}{cot45°}\) - \(\frac{cos30°}{sin90°}\)

Answer 1

 \(\frac{sin30°}{sin45°}\) + \(\frac{tan45°}{sec60°}\) - \(\frac{sin60°}{cot45°}\) - \(\frac{cos30°}{sin90°}\)

= \(\frac{\frac{1}2}{\frac{1}{\sqrt2}}\) + \(\frac{1}2\) - \(\frac{\frac{\sqrt3}2}1\) - \(\frac{\frac{\sqrt3}2}1\)

= \(\frac{1}{\sqrt2}\) + \(\frac{1}2\) - \(\frac{2\sqrt2}2\) = \(\frac{\sqrt2+1-2\sqrt3}2\)