Question

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

Answer 1

Combine ln terms and then the trig terms to get `ln(|tantheta|)`

Explanation:

Let's first look at the original:

`ln|sintheta|-ln|costheta|`

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

`ln(|sintheta|/|costheta|)`

Remember that `(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(|tantheta|)`