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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![**Simplifying Trigonometric Expressions Using Formulas**
To simplify the expression \(\cos(x + y) \cos(x - y)\), we can apply trigonometric addition and subtraction formulas.
### Expression:
\[
\cos(x + y) \cos(x - y)
\]
### Trigonometric Identities:
The product-to-sum identities in trigonometry are particularly useful here. For cosine, the relevant identity is:
\[
\cos(x + y) \cos(x - y) = \frac{1}{2} [\cos(2x) + \cos(2y)]
\]
### Simplified Expression:
Applying the identity, we simplify the original expression to:
\[
\frac{1}{2} [\cos(2x) + \cos(2y)]
\]
This transformation helps in evaluating the expression more easily and is useful in various applications within mathematics and physics.
---
This educational breakdown demonstrates the use of trigonometric identities to simplify expressions effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12cd5ca0-307a-4b4d-a33b-ad825a4575c3%2F3bea5f17-8514-45d9-b011-8829f2905ac9%2Fvwi6hmz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Simplifying Trigonometric Expressions Using Formulas**
To simplify the expression \(\cos(x + y) \cos(x - y)\), we can apply trigonometric addition and subtraction formulas.
### Expression:
\[
\cos(x + y) \cos(x - y)
\]
### Trigonometric Identities:
The product-to-sum identities in trigonometry are particularly useful here. For cosine, the relevant identity is:
\[
\cos(x + y) \cos(x - y) = \frac{1}{2} [\cos(2x) + \cos(2y)]
\]
### Simplified Expression:
Applying the identity, we simplify the original expression to:
\[
\frac{1}{2} [\cos(2x) + \cos(2y)]
\]
This transformation helps in evaluating the expression more easily and is useful in various applications within mathematics and physics.
---
This educational breakdown demonstrates the use of trigonometric identities to simplify expressions effectively.
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