Trigonometric identities: $ \frac{1+\cos(a)}{1-\cos(a)} + \frac{1-\cos(a)}{1+\cos(a)} = 2+4\cot^2(a)$ I don't really know how to begin, so if I'm missing some information please let me know what it is and I'll fill you guys in :).
This is the question I can't solve:
$$
\frac{1+\cos(a)}{1-\cos(a)} + \frac{1-\cos(a)}{1+\cos(a)} = 2+4\cot^2(a)       
$$
I need to prove their trigonometric identities.
I have the $5$ basic set of rules, I could write them all here but I suppose it's not needed, if it is please let me know since it's not gonna be simple to type.
I have over $40$ questions like these and I just couldn't seem to understand how to prove them equal, my best was $4 \cot^2(a) = 2 + 4 \cot^2(a)$
Thanks for everything!

Put $t=\tan (\frac a2)$.You have $$\frac{1+\cos(a)}{1-\cos(a)}=\frac{1+\frac{1-t^2}{1+t^2}}{1-\frac{1-t^2}{1+t^2}}=\frac{1}{t^2}$$
Besides $\cot(a)=\frac{1-t^2}{2t}$ so we have to prove
$$\frac{1}{t^2}+t^2=2+4\left(\frac{1-t^2}{2t}\right)^2$$
Immediate calculation gives $$\frac{1+t^4}{t^2}=\frac{1+t^4}{t^2}$$ which is obviously true.
