Question

How do you rewrite the expression as a single logarithm and simplify `lnabs(cosx)-lnabssinx`?

Answer 1

`ln|cotx|`

Explanation:

We have by the rule `lna - lnb = ln(a/b)`:

`=ln|cosx/sinx|`

By the identity `cotx = 1/tanx = 1/(sinx/cosx) = cosx/sinx`:

`=ln|cotx|`

Hopefully this helps!