# Establish the identity. ln |cot u| = ln |cos u| - ln |sin u| ____________________ Could someone please explain to me how to solve this?

Aug 3, 2018

Simply use $\ln \left(a\right) - \ln \left(b\right) = \ln \left(\frac{a}{b}\right)$.

$\ln | \cot u | = \ln | \cos \frac{u}{\sin} u |$

Now the logarithms cancel out

$\cot u = \cos \frac{u}{\sin} u$

$\frac{1}{\tan} u = \cos \frac{u}{\sin} u$

$\frac{1}{\sin \frac{u}{\cos} u} = \cos \frac{u}{\sin} u$

$\cos \frac{u}{\sin} u = \cos \frac{u}{\sin} u$

Hopefully this helps!