Solution :
The value of sin 15 degrees is \(\sqrt{3} – 1\over 2\sqrt{2}\).
Proof :
We will write sin 15 as sin (45 – 30).
By using formula sin (A – B) = sin A cos B – cos A sin B,
sin (45 – 30) = sin 45 cos 30 – cos 45 sin 30
\(\implies\) sin 15 = \(1\over \sqrt{2}\) \(\times\) \(\sqrt{3}\over 2\) – \(1\over \sqrt{2}\) \(\times\) \(1\over 2\)
\(\implies\) sin 15 = \(\sqrt{3} – 1\over 2\sqrt{2}\)
