# What is the Value of Sin 72 Degrees ?

## Solution :

The value of sin 72 degrees is $$\sqrt{10 + 2\sqrt{5}}\over 4$$.

Proof :

We know that value of cos 18 degrees is $$\sqrt{10 + 2\sqrt{5}}\over 4$$.

Since 72 degree is the complement of 18 degree.

$$\therefore$$ sin 72 = sin(90 – 18) = cos 18 = $$\sqrt{10 + 2\sqrt{5}}\over 4$$

Hence, sin 72 degrees is $$\sqrt{10 + 2\sqrt{5}}\over 4$$.