# What is the Value of Cos 18 Degrees ?

## 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 $$\sqrt{10 + 2\sqrt{5}}\over 4$$.