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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?

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up vote 5 down vote accepted

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

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