Prove an equation (complex numbers)

Prove an equation (complex numbers)

How can i prove this equation?
$$ {(1 + i\tan(x))^n \over (1-i\tan(x))^n} = {1 + i\tan(nx) \over
1-i\tan(nx)} , n \in N$$
I tried to use a binomial theorem to open brackets, but it did not help.