Solution :
The value of sin 75 degrees is \(\sqrt{3} + 1\over 2\sqrt{2}\).
Proof :
We will write sin 75 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 75 = \(1\over \sqrt{2}\) \(\times\) \(\sqrt{3}\over 2\) + \(1\over \sqrt{2}\) \(\times\) \(1\over 2\)
\(\implies\) sin 75 = \(\sqrt{3} + 1\over 2\sqrt{2}\)