Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$\ln | \cot x | =$ ?
A) $\frac { \ln | \sin x | } { \ln | \cos x | }$
B) $\frac { \ln | \cos x | } { \ln | \sin x | }$
C) $\ln | \sin x | - \ln | \cos x |$
D) $\ln | \cos x | - \ln | \sin x |$

Question

Quizplus · Accepted Answer

The identity $\ln | \cot x | = \ln | \cos x | - \ln | \sin x |$ is derived from the properties of logarithms and the definition of cotangent, where $\cot x = \frac{\cos x}{\sin x}$. Applying the logarithm property $\ln \frac{a}{b} = \ln a - \ln b$, we get the correct identity.

Choose the One Alternative That Best Completes the Statement or Answers