Hey guys.

In the following problem, I'm supposed to perform the addition and then use the fundamental identities to simplify.

Also please be loose on the format of the problem. I'm not very familiar with LaTeX at this point in time.

(1/(1 + cos x)) + (1/(1 - cos x))

What I did, since they had different denominators, I multiplied every fraction with (1 + cos x)(1 - cos x), eliminating the fractions and leaving me with

(1 - cos x) + (1 + cos x)

Thing is though, the answer is

, and the only thing I can do to the problem as I have it now is cancel the cos x and leave me with 2, which is obviously wrong. How is my thinking flawed on this problem?

I appreciate any and all help contributed.