Question

Verify the Identity. $$\ln \cot x=-\ln \tan x$$

   Verify the Identity.
$$\ln \cot x=-\ln \tan x$$

Precalculus: Functions and Graphs

Precalculus: Functions and Graphs

Earl W. Swokowski,… 11th Edition

Chapter 6, Problem 47

Instant Answer

Solved by Expert Babita Kumari

12/07/2020

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Verify the Identity. $$\ln \cot x=-\ln \tan x$$

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Key Concepts

Reciprocal Trigonometric Identities

Reciprocal trigonometric identities show the relationship between certain trigonometric functions. Specifically, the identity cot(x) = 1/tan(x) is crucial because it connects cotangent and tangent, permitting the use of logarithm properties to establish the relationship ln(cot x) = -ln(tan x).

Logarithm Properties

Logarithm properties are essential in simplifying expressions and proving identities. Particularly, the property ln(1/x) = -ln(x) allows one to convert the logarithm of a reciprocal into a negative logarithm, which is central to verifying the given identity.

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