Use the fundamental identities to simplify the expression. (There is more than one correct form of the answ cos(-x) sec(x) 2 cos(x) X
Use the fundamental identities to simplify the expression. (There is more than one correct form of the answ cos(-x) sec(x) 2 cos(x) 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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![## Simplifying Trigonometric Expressions Using Fundamental Identities
Use the fundamental identities to simplify the expression.
### Problem Statement:
\[ \cos\left(\frac{\pi}{2} - x\right) \sec(x) \]
### Attempted Solution:
The given answer in the solution box is:
\[ \text{COS}(x) \]
There is a red "X" mark indicating that the provided answer is incorrect.
### Analysis:
To simplify the expression, use the trigonometric identities:
1. **Co-Function Identity for Sine and Cosine:**
\[ \cos\left(\frac{\pi}{2} - x\right) = \sin(x) \]
2. **Secant and Cosine Relationship:**
\[ \sec(x) = \frac{1}{\cos(x)} \]
Now, rewrite the original expression using these identities:
\[ \cos\left(\frac{\pi}{2} - x\right) \sec(x) = \sin(x) \cdot \frac{1}{\cos(x)} \]
This simplifies to:
\[ \frac{\sin(x)}{\cos(x)} = \tan(x) \]
Hence, the simplified form of the expression is:
\[ \tan(x) \]
In summary, the correct form involves recognizing the trigonometric identities and correctly applying them to simplify the given expression. The attempted solution of \(\text{COS}(x)\) does not properly simplify the given trigonometric expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2Fbb457623-d58b-4920-9459-ee6ed44f8f12%2Fodh2zx9_processed.png&w=3840&q=75)
Transcribed Image Text:## Simplifying Trigonometric Expressions Using Fundamental Identities
Use the fundamental identities to simplify the expression.
### Problem Statement:
\[ \cos\left(\frac{\pi}{2} - x\right) \sec(x) \]
### Attempted Solution:
The given answer in the solution box is:
\[ \text{COS}(x) \]
There is a red "X" mark indicating that the provided answer is incorrect.
### Analysis:
To simplify the expression, use the trigonometric identities:
1. **Co-Function Identity for Sine and Cosine:**
\[ \cos\left(\frac{\pi}{2} - x\right) = \sin(x) \]
2. **Secant and Cosine Relationship:**
\[ \sec(x) = \frac{1}{\cos(x)} \]
Now, rewrite the original expression using these identities:
\[ \cos\left(\frac{\pi}{2} - x\right) \sec(x) = \sin(x) \cdot \frac{1}{\cos(x)} \]
This simplifies to:
\[ \frac{\sin(x)}{\cos(x)} = \tan(x) \]
Hence, the simplified form of the expression is:
\[ \tan(x) \]
In summary, the correct form involves recognizing the trigonometric identities and correctly applying them to simplify the given expression. The attempted solution of \(\text{COS}(x)\) does not properly simplify the given trigonometric expression.
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