Solution :
The value of cos 75 degrees is \(\sqrt{3} – 1\over 2\sqrt{2}\).
Proof :
We will write cos 75 as cos (45 + 30).
By using formula cos (A + B) = cos A cos B – sin A sin B,
cos (45 + 30) = cos 45 cos 30 – sin 45 sin 30
\(\implies\) cos 75 = \(1\over \sqrt{2}\) \(\times\) \(\sqrt{3}\over 2\) – \(1\over \sqrt{2}\) \(\times\) \(1\over 2\)
\(\implies\) cos 75 = \(\sqrt{3} – 1\over 2\sqrt{2}\)
