I need help with this. I've gotten a few steps so far but I cannot figure out the rest. ## Prove the IdentityGiven the trigonometric identity to prove:\[ \sec(-x) - \sin(-x) \tan(-x) = \cos x \]### NoteEach statement must be based on a rule chosen from the Rule menu. To see a detailed description of a rule, select the More Information Button to the right of the rule.### Steps and Corresponding Rules| Statement | Rule ||------------------------------------------------|-----------|| $\sec(-x) - \sin(-x) \tan(-x)$ | || $\sec(-x) - \sin(-x) \tan(-x)$ | Algebra || $\sec x - \sin(-x) \tan(-x)$ | Odd/Even || $\sec x - (-\sin x) \tan(-x)$ | Odd/Even || $\sec x - (-\sin x) (-\tan x)$ | Odd/Even || $\sec x - \sin x \tan x$ | Simplify || $\boxed{\cos x}$ | Identity |### Explanation of the Rules:- **Algebra**: Simplifying the expression.- **Odd/Even**: Applying properties of sine, cosine, and tangent for negative angles.- **Simplify**: Reducing the expression to its simplest form.- **Identity**: Using a fundamental trigonometric identity to conclude the proof.### Diagram ExplanationTo the right of the rule table, there is a selection menu which allows for the application of various trigonometric rules:- The vertical scroll list includes different trigonometric rules and identities.- Symbols such as $\cos$, $\sin$, $\tan$, $\cot$, $\sec$, $\csc$, $\pi$, parentheses, and square roots allow for selecting specific trigonometric functions and constants.- Additional buttons include a help icon (?), a reset button (↻), and a validation button (X).

Answered: Prove the identity. sec (-x) – sin(-x)…

Math

Trigonometry

Prove the identity. sec (-x) – sin(-x) tan(-x) = cosx

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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Question

I need help with this. I've gotten a few steps so far but I cannot figure out the rest.

## Prove the Identity

Given the trigonometric identity to prove:
\[ \sec(-x) - \sin(-x) \tan(-x) = \cos x \]

### Note
Each statement must be based on a rule chosen from the Rule menu. To see a detailed description of a rule, select the More Information Button to the right of the rule.

### Steps and Corresponding Rules

| Statement | Rule |
|------------------------------------------------|-----------|
| $\sec(-x) - \sin(-x) \tan(-x)$ | |
| $\sec(-x) - \sin(-x) \tan(-x)$ | Algebra |
| $\sec x - \sin(-x) \tan(-x)$ | Odd/Even |
| $\sec x - (-\sin x) \tan(-x)$ | Odd/Even |
| $\sec x - (-\sin x) (-\tan x)$ | Odd/Even |
| $\sec x - \sin x \tan x$ | Simplify |
| $\boxed{\cos x}$ | Identity |

### Explanation of the Rules:
- **Algebra**: Simplifying the expression.
- **Odd/Even**: Applying properties of sine, cosine, and tangent for negative angles.
- **Simplify**: Reducing the expression to its simplest form.
- **Identity**: Using a fundamental trigonometric identity to conclude the proof.

### Diagram Explanation
To the right of the rule table, there is a selection menu which allows for the application of various trigonometric rules:
- The vertical scroll list includes different trigonometric rules and identities.
- Symbols such as $\cos$, $\sin$, $\tan$, $\cot$, $\sec$, $\csc$, $\pi$, parentheses, and square roots allow for selecting specific trigonometric functions and constants.
- Additional buttons include a help icon (?), a reset button (↻), and a validation button (X).

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