COS X 3) sec x + tan x = 1 - sin x
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
![### Expression Analysis
The mathematical expression given is:
\[ \text{3) } \sec x + \tan x = \frac{\cos x}{1 - \sin x} \]
**Explanation:**
- **Secant and Tangent Functions**: In trigonometry, \(\sec x\) is the secant of angle \(x\), which is the reciprocal of \(\cos x\), and \(\tan x\) is the tangent, which is the ratio of \(\sin x\) to \(\cos x\).
- **Right Side of the Equation**: The right side of the equation is a fraction where the numerator is \(\cos x\) and the denominator is \(1 - \sin x\).
This equation involves trigonometric identities and may be simplified or used in solving for specific values of \(x\) that satisfy it.
**Possible Applications:**
- This equation might be used in algebraic manipulation or trigonometric identity proofs.
- Understanding how to transform one side of the equation into the other could aid in solving advanced trigonometric equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f9e96de-8215-4532-a7d0-6f1fdf87f241%2F2f6b3e75-0c2f-4edc-8734-76a553a07950%2Fjx3bxgo_processed.png&w=3840&q=75)
Transcribed Image Text:### Expression Analysis
The mathematical expression given is:
\[ \text{3) } \sec x + \tan x = \frac{\cos x}{1 - \sin x} \]
**Explanation:**
- **Secant and Tangent Functions**: In trigonometry, \(\sec x\) is the secant of angle \(x\), which is the reciprocal of \(\cos x\), and \(\tan x\) is the tangent, which is the ratio of \(\sin x\) to \(\cos x\).
- **Right Side of the Equation**: The right side of the equation is a fraction where the numerator is \(\cos x\) and the denominator is \(1 - \sin x\).
This equation involves trigonometric identities and may be simplified or used in solving for specific values of \(x\) that satisfy it.
**Possible Applications:**
- This equation might be used in algebraic manipulation or trigonometric identity proofs.
- Understanding how to transform one side of the equation into the other could aid in solving advanced trigonometric equations.
Transcribed Image Text:**Verify that each equation is an identity.**
This statement suggests that you should confirm whether each given equation holds true for all values of the variables within it. An identity is an equation that is always true, regardless of the values of any variables. This is often a topic explored in algebra and trigonometry. The explanatory or instructional text will guide you through the verification process by substituting or transforming the equations as needed to demonstrate their truthfulness universally.
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