Trig proof

Hello, i tried to prove the following trigonometric problem from a textbook but i think the equation doesn't hold. Can anyone confirm it?

So the domain of the angle is 3π/2 < x < 2π , and the equation is:

sqrt((1+cos(x))/(1-cos(x)))+sqrt((1-cos(x))/(1+cos(x))) = -2cot(x)

First I need to work out your backets.  Some spacing woud have been nice.

sqrt (  [1+cos(x)]    /  [1-cos(x)] )      +   sqrt(  [1-cos(x)]  / [1+cos(x)] ) = -2cot(x)

\(\sqrt\frac{1+cos(x)}{1-cos(x)}+\sqrt{\frac{1-cos(x)}{1+cos(x)}} = -2cot(x)\)

Is this what you are asking us to try and prove?

Here are the 2 graphs, you can see that they are not the same.  Not even in the given domain.

This question has been posed twice.

See the answer from the other (later) submission.