Hey guys I've been working on this one trig identity for about an hour and I can't seem to make it work it out. Any help will be appreciated

(tan/1+cos) + (sin/1-cos) = cos + sec*csc

The identity is equal to cot(x)+csc(x)sec(x), not cos(x).

\frac{tan(x)}{1+cos(x)}+\frac{sin(x)}{1-cos(x)}

You can cross multiply, this gives:

\frac{tan(x)-tan(x)cos(x)+sin(x)+cos(x)sin(x)}{sin^{2}(x)}

Now, if you expand and simplify each, you will whittle it down to the right side.

Which is cot(x)+csc(x)sec(x). Having that cos(x) in there may have been the problem.