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