verify : [sec(x) / csc(x) - cot(x)] - [sec(x) / csc(x) + cot(x)] = 2csc(x)

Answer 1

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 right-hand-side, I find the given identity not true.

Answer 2

i put it in my graphing calculator, though, and they graph the same function

Answer 3

This is why I suspected there is a typo.
The left-hand-side evaluates to -2csc(x).
The right-hand-side, 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

Answer 4

The left-hand-side evaluates to -2cot(x).