Verify each identity. (cosx)/(1-sinx)=secx+tanx

Name: Problem 9, Chapter 3: College Trigonometry
Uploaded: 2020-07-08T17:42:28-08:00
Duration: 1 min 28 s
Channel: Himanshu Kushwaha
Description: Verify each identity. (cosx)/(1-sinx)=secx+tanx

Key Concepts

Rationalization of Trigonometric Expressions

This concept involves multiplying the numerator and denominator of a trigonometric fraction by a conjugate or a strategically chosen expression to simplify the overall form. In many trigonometric proofs, rationalization is used to eliminate complex denominators or to transform the expression into a sum or difference of simpler trigonometric functions, easing the verification of the identity.

Pythagorean Identities

Pythagorean identities are fundamental relations among sine, cosine, and other trigonometric functions. For example, the identity sin²x + cos²x = 1 can be rearranged to express 1 - sin²x as cos²x. This manipulation is crucial in proofs where a difference of squares appears, allowing the expression to be rewritten in a form that reveals underlying simplifications.

Reciprocal and Quotient Identities

These identities define relationships such as sec x = 1/cos x and tan x = sin x/cos x. They are essential in trigonometry for converting between different trigonometric functions. In many proofs, including verifying identities, these relationships are used to rewrite expressions in equivalent forms that simplify the process of demonstrating equivalence.

Algebraic Manipulation in Trigonometry

General algebraic techniques such as factoring, expanding, and splitting fractions are vital for the simplification and transformation of trigonometric expressions. These methods allow the breaking down of complex expressions into sums, differences, or products of familiar trigonometric functions, thereby facilitating the comprehensive understanding and verification of trigonometric identities.

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