Establish the identity. (4 cos 0-2 sin 0)2 + (2 cos 0 +4 sin 0)2 = 20 %3D Rewrite the left side by removing the parentheses. + 4 cos 20+ 16 cos 0 sin 0+ 16 sin 0 (Simp
Establish the identity. (4 cos 0-2 sin 0)2 + (2 cos 0 +4 sin 0)2 = 20 %3D Rewrite the left side by removing the parentheses. + 4 cos 20+ 16 cos 0 sin 0+ 16 sin 0 (Simp
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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![**Establish the Identity:**
\[
(4 \cos \theta - 2 \sin \theta)^2 + (2 \cos \theta + 4 \sin \theta)^2 = 20
\]
Rewrite the left side by removing the parentheses:
\[
+ 4 \cos^2 \theta + 16 \cos \theta \sin \theta + 16 \sin^2 \theta
\]
**Step-by-step Explanation:**
1. Expand \( (4 \cos \theta - 2 \sin \theta)^2 \) and \( (2 \cos \theta + 4 \sin \theta)^2 \).
2. Use the identities for expanding squares: \( a^2 + 2ab + b^2 \).
3. Combine like terms to simplify the expression.
Solution involves verifying that the expanded expression simplifies to equal 20, confirming the identity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30d03622-fa18-4c63-ac70-0fc0cf98f1dc%2Fe2c5fd8d-ec9a-4d04-9c7c-666f32e394be%2Fvwfe6i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Establish the Identity:**
\[
(4 \cos \theta - 2 \sin \theta)^2 + (2 \cos \theta + 4 \sin \theta)^2 = 20
\]
Rewrite the left side by removing the parentheses:
\[
+ 4 \cos^2 \theta + 16 \cos \theta \sin \theta + 16 \sin^2 \theta
\]
**Step-by-step Explanation:**
1. Expand \( (4 \cos \theta - 2 \sin \theta)^2 \) and \( (2 \cos \theta + 4 \sin \theta)^2 \).
2. Use the identities for expanding squares: \( a^2 + 2ab + b^2 \).
3. Combine like terms to simplify the expression.
Solution involves verifying that the expanded expression simplifies to equal 20, confirming the identity.
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