Trigonometric Identities

1-cosx/sinx - sinx/1-cosx = 2cscx

First, recognize that
csc(x) = 1/sin(x)

Also, note that sin^2(x) + cos^2(x) = 1

The usual approach to solving this type of problem is to expand everything on the left in terms of sines and cosines. You then manipulate the result algebraically until you get 2/sin(x) which is equal to 2csc(x). You will, if you don't make any mistakes.