tan(-0) csc 0 14 tan 0

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Simplify the expression. Answers should have no quotient.

The mathematical expression is:

\[
\frac{\tan(-\theta) \csc^2 \theta}{1 + \tan^2 \theta}
\]

### Explanation:

This expression contains trigonometric functions:

- **Tan (-θ):** Represents the tangent function with a negative angle.
- **Csc² θ:** Represents the cosecant function squared, which is the reciprocal of the sine function.
- **1 + Tan² θ:** This can also be interpreted using the trigonometric identity related to sec² θ, where 1 + tan² θ = sec² θ.

This formula encapsulates a combination of these functions, potentially useful for solving trigonometric identities or calculus problems.
Transcribed Image Text:The mathematical expression is: \[ \frac{\tan(-\theta) \csc^2 \theta}{1 + \tan^2 \theta} \] ### Explanation: This expression contains trigonometric functions: - **Tan (-θ):** Represents the tangent function with a negative angle. - **Csc² θ:** Represents the cosecant function squared, which is the reciprocal of the sine function. - **1 + Tan² θ:** This can also be interpreted using the trigonometric identity related to sec² θ, where 1 + tan² θ = sec² θ. This formula encapsulates a combination of these functions, potentially useful for solving trigonometric identities or calculus problems.
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