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 \(\sqrt{10 + 2\sqrt{5}}\over 4\).

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