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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Question
![**Verify the Identity:**
Given Expression:
\[ 7 \cos^2 B - 7 \sin^2 B = 14 \cos^2 B - 7 \]
Step-by-Step Verification:
1. Start with the Left-Hand Side (LHS):
\[ 7 \cos^2 B - 7 \sin^2 B \]
2. Factor out 7 from the expression:
\[ = 7 (\cos^2 B - \sin^2 B) \]
3. Use the Pythagorean identity \((\sin^2 B = 1 - \cos^2 B)\):
\[ = 7 \cos^2 B - 7 (1 - \cos^2 B) \]
4. Expand the equation:
\[ = 7 \cos^2 B - 7 + 7 \cos^2 B \]
5. Simplify further:
\[ = 14 \cos^2 B - 7 \]
This completes the verification, confirming that the given expression is an identity.
No graphs or diagrams are included in this image, aside from an abstract red sketch on the right, which appears unrelated to the mathematical content.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90e413d6-0f95-45bc-9120-3de888a1b336%2F0c2697b9-4284-466c-b31d-8116f88f90ca%2Fdxtbkqu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Verify the Identity:**
Given Expression:
\[ 7 \cos^2 B - 7 \sin^2 B = 14 \cos^2 B - 7 \]
Step-by-Step Verification:
1. Start with the Left-Hand Side (LHS):
\[ 7 \cos^2 B - 7 \sin^2 B \]
2. Factor out 7 from the expression:
\[ = 7 (\cos^2 B - \sin^2 B) \]
3. Use the Pythagorean identity \((\sin^2 B = 1 - \cos^2 B)\):
\[ = 7 \cos^2 B - 7 (1 - \cos^2 B) \]
4. Expand the equation:
\[ = 7 \cos^2 B - 7 + 7 \cos^2 B \]
5. Simplify further:
\[ = 14 \cos^2 B - 7 \]
This completes the verification, confirming that the given expression is an identity.
No graphs or diagrams are included in this image, aside from an abstract red sketch on the right, which appears unrelated to the mathematical content.
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