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