Verify the following is an identity: (cos(2 x)+sin^2 x)/(1-cos^2 x)=cot^2(x).

Name: Problem 38, Chapter 9: Precalculus
Uploaded: 2020-12-19T11:26:40-08:00
Duration: 1 min 48 s
Channel: Harmender Singh Yadav
Description: Verify the following is an identity: (cos(2 x)+sin^2 x)/(1-cos^2 x)=cot^2(x).

step 1 In this question we have to verify the identity. Cosine 2x plus sine square x divided by 1 minus

Verify the following is an identity: (cos(2 x)+sin^2...

Key Concepts

Definition of Cotangent

Cotangent is defined as the ratio of the cosine function to the sine function, expressed as cot x = cos x/sin x. This definition is essential for transforming expressions into forms where the cotangent function appears, and it facilitates direct comparisons and simplifications in the context of verifying trigonometric identities.

Pythagorean Identity

The Pythagorean identity, which states that sin^2 x + cos^2 x = 1, is a foundational relationship in trigonometry. It allows for the substitution and re-expression of trigonometric functions in terms of one another, enabling the simplification of expressions and the verification of identities by relating different trigonometric quantities.

Double-Angle Formula

The double-angle formulas are specific trigonometric identities that express trigonometric functions of twice an angle in terms of functions of the original angle. For cosine, the double-angle formula can be written in multiple forms, and choosing the appropriate one simplifies expressions and proofs, such as by expressing cos(2x) in terms of sin^2 x or cos^2 x.

Trigonometric Identities

Trigonometric identities are fundamental equations involving trigonometric functions that hold true for all values within their domains. They are used to simplify and transform expressions, and to prove other trigonometric relationships. Recognizing and applying these identities is crucial for manipulating complex trigonometric expressions and verifying equations within trigonometry.

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