Prove the identity. cos?x cscx+1 1- sinx cscx

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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## Prove the Identity

\[ \frac{\cos^2 x}{1 - \sin x} = \frac{\csc x + 1}{\csc x} \]

Note that 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.

### Step-by-Step Solution

1. **Statement**

\[ \frac{\cos^2 x}{1 - \sin x} \]

**Rule**: [Select Rule]

\[ = \]

[Input Box]

2. **Validate Button**

*Click on the "Validate" button to check if the proven step is correct.*

### Rule Selection Menu
A visual menu is displayed showing various mathematical symbols and functions that can be selected to help prove the identity. Available symbols and functions include:

- \[ \Box, \Box^2, \Box^3 \]
- \[ \Box, \Box, \sqrt{\Box} \]
- \[ \cos, \sin, \tan \]
- \[ \cot, \sec, \csc \]
- \[ \pi \]
- \[ (\Box) \]
- \[ \frac{\Box}{\Box} \]
- and more.

Use these symbols and functions to select the appropriate rule for each transformation step. For more information about each rule, click the “?” button.
Transcribed Image Text:## Prove the Identity \[ \frac{\cos^2 x}{1 - \sin x} = \frac{\csc x + 1}{\csc x} \] Note that 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. ### Step-by-Step Solution 1. **Statement** \[ \frac{\cos^2 x}{1 - \sin x} \] **Rule**: [Select Rule] \[ = \] [Input Box] 2. **Validate Button** *Click on the "Validate" button to check if the proven step is correct.* ### Rule Selection Menu A visual menu is displayed showing various mathematical symbols and functions that can be selected to help prove the identity. Available symbols and functions include: - \[ \Box, \Box^2, \Box^3 \] - \[ \Box, \Box, \sqrt{\Box} \] - \[ \cos, \sin, \tan \] - \[ \cot, \sec, \csc \] - \[ \pi \] - \[ (\Box) \] - \[ \frac{\Box}{\Box} \] - and more. Use these symbols and functions to select the appropriate rule for each transformation step. For more information about each rule, click the “?” button.
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