Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Trigonometric Identity Proof
**Problem 4:**
Prove the following identity:
\[
\frac{\sec \theta + \tan \theta}{\cot \theta + \cos \theta} = \tan \theta \sec \theta
\]
**Approach and Explanation:**
To prove this identity, consider using basic trigonometric identities such as:
- \(\sec \theta = \frac{1}{\cos \theta}\)
- \(\tan \theta = \frac{\sin \theta}{\cos \theta}\)
- \(\cot \theta = \frac{1}{\tan \theta}\)
- \(\cos \theta = \cos \theta\)
These identities can help transform the given expression step-by-step into the form on the right-hand side. Manipulation of these identities can simplify the expression and prove the equality.
The goal is to simplify both sides of the equation strategically and demonstrate that one side can be transformed into the other using the fundamental trigonometric identities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe708b20e-246d-43f9-aec0-b076b54d250e%2Fd3351f8a-bd34-49ae-ba8e-faf12166b6a7%2Fqvroh4u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometric Identity Proof
**Problem 4:**
Prove the following identity:
\[
\frac{\sec \theta + \tan \theta}{\cot \theta + \cos \theta} = \tan \theta \sec \theta
\]
**Approach and Explanation:**
To prove this identity, consider using basic trigonometric identities such as:
- \(\sec \theta = \frac{1}{\cos \theta}\)
- \(\tan \theta = \frac{\sin \theta}{\cos \theta}\)
- \(\cot \theta = \frac{1}{\tan \theta}\)
- \(\cos \theta = \cos \theta\)
These identities can help transform the given expression step-by-step into the form on the right-hand side. Manipulation of these identities can simplify the expression and prove the equality.
The goal is to simplify both sides of the equation strategically and demonstrate that one side can be transformed into the other using the fundamental trigonometric identities.
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