# How do you rewrite the expression as a single log and simplify ln|sin θ| - ln|cos θ|?

Combine ln terms and then the trig terms to get $\ln \left(| \tan \theta |\right)$

#### Explanation:

Let's first look at the original:

$\ln | \sin \theta | - \ln | \cos \theta |$

The first thing we can do is combine the two $\ln$ terms:

$\ln \left(| \sin \theta \frac{|}{|} \cos \theta |\right)$

Remember that $\frac{\sin}{\cos} = \tan$ Let's also see that, by taking the absolute values of both sin and cos, tan is forced to be positive, so we can now say:

$\ln \left(| \tan \theta |\right)$