Question

How do you verify the identity `lnabs(csctheta+cottheta)+lnabs(csctheta-cottheta)=0`?

Answer 1

See below.

Explanation:

After

`(Csc(x) + Cot(x)) (Csc(x) - Cot(x)) = 1`

It follows

`log(abs((Csc(x) + Cot(x)) (Csc(x) - Cot(x)))=`

`=log abs(Csc(x) + Cot(x))+log abs (Csc(x) - Cot(x))=0`