Rewrite $\ln | \sin \theta | - \ln | \cos \theta |$ as a single logarithm and then simplify the result.
A) $\ln | \cos \theta |$
B) $\ln | \csc \theta |$
C) $\ln | \sec \theta |$
D) $\ln | \tan \theta |$
E) $\ln | \sin \theta |$

Question

Rewrite $\ln | \sin \theta | - \ln | \cos \theta |$ as a single logarithm and then simplify the result.  
A)  $\ln | \cos \theta |$
B)  $\ln | \csc \theta |$
C)  $\ln | \sec \theta |$
D)  $\ln | \tan \theta |$
E)  $\ln | \sin \theta |$

Quizplus · Accepted Answer

The expression can be simplified using the logarithm property $\ln a - \ln b = \ln \left(\frac{a}{b}\right)$, resulting in $\ln \left|\frac{\sin \theta}{\cos \theta}\right|$, which simplifies to $\ln |\tan \theta|$.

Rewrite ln⁡∣sin⁡θ∣−ln⁡∣cos⁡θ∣\ln | \sin \theta | - \ln | \cos \theta |ln∣sinθ∣−ln∣cosθ∣

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