Trigonometric Identity $\frac{1}{1-\cos t} + \frac{1}{1+\cos t}$ I am just learning about trig identities, and after doing a few, I am stuck on this one:
$$
\frac{1}{1-\cos t} + \frac{1}{1+\cos t}.
$$
The only way to start, that I can think of is this:
$$
\frac{1}{1-(1/\sec t)} + \frac{1}{1+(1/\sec t)}.
$$
And from there it just gets messed up.  Can someone point me in the right direction?

Hint:
Use that 
$$
\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}
$$
along with the identity
$$
\sin^2t+\cos^2t=1.
$$
