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

Mar 2, 2017

$\ln | \cot x |$

#### Explanation:

We have by the rule $\ln a - \ln b = \ln \left(\frac{a}{b}\right)$:

$= \ln | \cos \frac{x}{\sin} x |$

By the identity $\cot x = \frac{1}{\tan} x = \frac{1}{\sin \frac{x}{\cos} x} = \cos \frac{x}{\sin} x$:

$= \ln | \cot x |$

Hopefully this helps!