Rewrite the expression as a single logarithm and simplify the result.
$\ln | \sec x | + \ln | \sin x |$
A) $\ln | \cos x |$
B) $\ln | \csc x |$
C) $\ln | \cot x |$
D) $\ln | \sin x |$
E) $\ln | \tan x |$

Question

Rewrite the expression as a single logarithm and simplify the result. 
 $\ln | \sec x | + \ln | \sin x |$  
A) $\ln | \cos x |$
B) $\ln | \csc x |$
C) $\ln | \cot x |$
D) $\ln | \sin x |$
E) $\ln | \tan x |$

Quizplus · Accepted Answer

Using the logarithmic property $\ln a + \ln b = \ln(ab)$, the expression simplifies to $\ln | \sec x \sin x |$. Since $\sec x = \frac{1}{\cos x}$, the expression becomes $\ln | \frac{\sin x}{\cos x} | = \ln | \tan x |$.

Rewrite the Expression as a Single Logarithm and Simplify the Result