Write the expression as a product of trigonometric functions. cs 6x - cos 2x cos 6x - cos 2x =
Write the expression as a product of trigonometric functions. cs 6x - cos 2x cos 6x - cos 2x =
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°.
Related questions
Question
![**Problem Statement:**
Write the expression as a product of trigonometric functions.
\[ \cos 6x - \cos 2x \]
---
**Solution:**
We need to express the difference \( \cos 6x - \cos 2x \) as a product of trigonometric functions using identities.
**Use the identity:**
\[ \cos A - \cos B = -2 \sin \left(\frac{A + B}{2}\right) \sin \left(\frac{A - B}{2}\right) \]
**Apply the identity:**
For \( A = 6x \) and \( B = 2x \):
\[ \cos 6x - \cos 2x = -2 \sin \left( \frac{6x + 2x}{2} \right) \sin \left( \frac{6x - 2x}{2} \right) \]
\[ = -2 \sin (4x) \sin (2x) \]
Thus, the expression becomes:
\[ \cos 6x - \cos 2x = -2 \sin 4x \sin 2x \]
This is the product form of the difference of cosines.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87f4f9f0-5746-4ade-a4d5-463157f8ae50%2Ffd5640e4-67ce-43c7-9c31-95c49815c456%2Fqo9lv3e_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Write the expression as a product of trigonometric functions.
\[ \cos 6x - \cos 2x \]
---
**Solution:**
We need to express the difference \( \cos 6x - \cos 2x \) as a product of trigonometric functions using identities.
**Use the identity:**
\[ \cos A - \cos B = -2 \sin \left(\frac{A + B}{2}\right) \sin \left(\frac{A - B}{2}\right) \]
**Apply the identity:**
For \( A = 6x \) and \( B = 2x \):
\[ \cos 6x - \cos 2x = -2 \sin \left( \frac{6x + 2x}{2} \right) \sin \left( \frac{6x - 2x}{2} \right) \]
\[ = -2 \sin (4x) \sin (2x) \]
Thus, the expression becomes:
\[ \cos 6x - \cos 2x = -2 \sin 4x \sin 2x \]
This is the product form of the difference of cosines.
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