What is the Value of Cos 36 Degrees ?

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 $\sqrt{5} + 1\over 4$.