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

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