Thread: Clarification

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|.

Originally Posted by kaiser0792

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|.

But

So

.

Thank you Prove IT, I knew it was an algebra step, but I've been deep into trig integrals and couldn't see the forest for the trees!