Solution :
The value of sin 36 degrees is \(\sqrt{10 – 2\sqrt{5}}\over 4\).
Proof :
We know that the value of cos 36 degrees is \(\sqrt{5} + 1\over 4\).
Putting \(\theta\) = 36 in \(cos \theta\) = \(\sqrt{1 – sin^2 \theta}\), we get
cos 36 = \(\sqrt{1 – sin^2 36}\) = \(\sqrt{1 – ({\sqrt{5} + 1\over 4})^2}\) = \(\sqrt{10 – 2\sqrt{5}}\over 4\)
Hence, cos 36 degrees is \(\sqrt{10 – 2\sqrt{5}}\over 4\).
