Solution :
The value of cos 18 degrees is \(\sqrt{10 + 2\sqrt{5}}\over 4\).
Proof :
We know that the value of sin 18 degrees is \(\sqrt{5} – 1\over 4\).
Putting \(\theta\) = 18 in \(cos \theta\) = \(\sqrt{1 – sin^2 \theta}\), we get
cos 18 = \(\sqrt{1 – sin^2 18}\) = \(\sqrt{1 – ({\sqrt{5} – 1\over 4})^2}\) = \(\sqrt{10 + 2\sqrt{5}}\over 4\)
Hence, cos 18 degrees is \(\sqrt{10 + 2\sqrt{5}}\over 4\).
