What is the Value of Cos 54 Degrees ?

Solution :

The value of cos 54 degrees is \(\sqrt{10 – 2\sqrt{5}}\over 4\).

Proof :

We know that value of sin 36 degrees is \(\sqrt{10 – 2\sqrt{5}}\over 4\).

Since 54 degree is the complement of 36 degree.

\(\therefore\) cos 54 = sin(90 – 36) = sin 36 = \(\sqrt{10 – 2\sqrt{5}}\over 4\)

Hence, cos 54 degrees is \(\sqrt{10 – 2\sqrt{5}}\over 4\).

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