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 \(\sqrt{5} + 1\over 4\).

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