Verify the identity. (1+sinx)/(1-sinx)=(tanx+secx)^2 |...

Name: Problem 86, Chapter 7: Precalculus Mathematics for Calculus
Uploaded: 2020-05-14T04:15:02-08:00
Duration: 2 min 4 s
Channel: Linh Vu
Description: Verify the identity. (1+sinx)/(1-sinx)=(tanx+secx)^2

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Key Concepts

Even Functions

Even functions are those that satisfy the property f(-x) = f(x) for every x in their domain. In the context of trigonometry, this property is exhibited by functions like cosine, allowing the replacement of the function evaluated at a negative angle with the same value at a positive angle, simplifying the manipulation of expressions and identities.

Odd Functions

Odd functions are characterized by the relation f(-x) = -f(x) for each x in their domain. This inherent symmetry, often seen in the sine function, means that the function’s value at a negative argument is the negative of its value at the corresponding positive argument, which is a useful property when simplifying trigonometric expressions.

Trigonometric Identity Verification

Verifying trigonometric identities involves systematically applying known properties and definitions, such as even and odd function characteristics, to demonstrate that two expressions are equivalent for all values in their domain. This process is fundamental in trigonometry and aids in simplifying complex expressions into more manageable forms.

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