This is not strictly a calculus problem, but a question about the form of a trigonometric integral.

Can someone tell me how -ln|csc x + cot x| is equal to ln|csc x - cot x|?

I know that using the properties of logarithms that

-ln|csc x + cot x| = ln (|csc x + cot x|)^-1 = ln |[1/(csc x + cot x)]|, but, I'm drawing a blank as to how any of these forms translates to

ln|csc x - cot x|.