How do I prove $\sec^2 \frac{a}{2}=\frac{2\sec a}{1+\sec a}$?

Question

I am stuck in the middle of proving this identity, please help!

$$\sec^2 \frac{a}{2}=\frac{2\sec a}{1+\sec a}$$

Answer 1

$$\sec^2(\frac{A}{2}) = \frac{1}{\cos^2(\frac{A}{2})} = \frac{2}{1+\cos(A)}=2\frac{\sec(A)}{1+\sec(A)}$$

The last equality holds because you can divide both the numerator and the denominator by $\cos(A)$.