# Find the Value of Tan 75 degrees ?

## 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 = $$1 + {1\over \sqrt{3}}\over 1 – {1\over \sqrt{3}}$$ = $$\sqrt{3} + 1\over \sqrt{3} – 1$$