Solution :
The value of tan 75 degrees is \(\sqrt{3} + 1\over \sqrt{3} – 1\).
Proof :
We write tan 75 as tan (45 + 30).
Using the formula of tan (A + B),
tan 75 = tan (45 + 30) = \(tan 45 + tan 30\over 1 – tan 45 tan 30\)
\(\implies\) tan 75 = \(1 + {1\over \sqrt{3}}\over 1 – {1\over \sqrt{3}}\) = \(\sqrt{3} + 1\over \sqrt{3} – 1\)