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