Solution :
The value of cos 36 degrees is \(\sqrt{5} + 1\over 4\).
Proof :
We know that the value sin 18 degrees is \(\sqrt{5} – 1\over 4\).
We have, \(cos 2\theta\) = \(1 – 2 sin^2 \theta\)
\(\therefore\) cos 36 = 1 – \(2 sin^2 18\)
\(\implies\) cos 36 = 1 – 2\(({\sqrt{5} – 1\over 4})^2\) = \(\sqrt{5} + 1\over 4\)
Hence, cos 36 degrees is \(\sqrt{5} + 1\over 4\).