trig
posted by briana .
verify : [sec(x) / csc(x)  cot(x)]  [sec(x) / csc(x) + cot(x)] = 2csc(x)

Use the following identities to express everything in sin(x), cos(x), tan(x) and cot(x):
sec(x)=1/cos(x)
csc(x)=1/sin(x)
Unless there is a typo on the righthandside, I find the given identity not true. 
i put it in my graphing calculator, though, and they graph the same function

This is why I suspected there is a typo.
The lefthandside evaluates to 2csc(x).
The righthandside, 2*csc(x).
I suggest you recheck the expressions posted.
Here's a plot of each side of the identity as posted.
http://img508.imageshack.us/img508/3851/1294005524.png 
The lefthandside evaluates to 2cot(x).