Now, simplify 4 cos² ß − 4(1 − cos² ß) by combining similar terms. 4 cos² ß - 4(1- cos² B) В = 4 cos² B + = 8 cos² ß - 4 X - 4
Now, simplify 4 cos² ß − 4(1 − cos² ß) by combining similar terms. 4 cos² ß - 4(1- cos² B) В = 4 cos² B + = 8 cos² ß - 4 X - 4
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°.
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![### Simplifying Expression by Combining Similar Terms
To simplify the expression \( 4 \cos^2 \beta - 4 \left( 1 - \cos^2 \beta \right) \) by combining similar terms, follow the steps outlined below:
1. **Distribute the -4**:
\[
4 \cos^2 \beta - 4 \left( 1 - \cos^2 \beta \right)
\]
becomes:
\[
4 \cos^2 \beta - 4 + 4 \cos^2 \beta
\]
2. **Combine similar terms**:
\[
4 \cos^2 \beta + 4 \cos^2 \beta - 4
\]
3. **Simplify the combined terms**:
The similar terms \( 4 \cos^2 \beta \) and \( 4 \cos^2 \beta \) add up to \( 8 \cos^2 \beta \):
\[
8 \cos^2 \beta - 4
\]
Therefore, the simplified expression is \( 8 \cos^2 \beta - 4 \).
### Detailed Explanation of Errors in the Original Process
- Initially, there is a mistake indicating a missing term after the distribution in the equation. The expression should have the distributed terms fully and properly combined.
### Correct Simplified Expression
So, the correct final simplified expression is:
\[
8 \cos^2 \beta - 4
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2F71635afc-8fa5-4c4a-8840-ec6e3be2e6c9%2Fqtpw6hs_processed.png&w=3840&q=75)
Transcribed Image Text:### Simplifying Expression by Combining Similar Terms
To simplify the expression \( 4 \cos^2 \beta - 4 \left( 1 - \cos^2 \beta \right) \) by combining similar terms, follow the steps outlined below:
1. **Distribute the -4**:
\[
4 \cos^2 \beta - 4 \left( 1 - \cos^2 \beta \right)
\]
becomes:
\[
4 \cos^2 \beta - 4 + 4 \cos^2 \beta
\]
2. **Combine similar terms**:
\[
4 \cos^2 \beta + 4 \cos^2 \beta - 4
\]
3. **Simplify the combined terms**:
The similar terms \( 4 \cos^2 \beta \) and \( 4 \cos^2 \beta \) add up to \( 8 \cos^2 \beta \):
\[
8 \cos^2 \beta - 4
\]
Therefore, the simplified expression is \( 8 \cos^2 \beta - 4 \).
### Detailed Explanation of Errors in the Original Process
- Initially, there is a mistake indicating a missing term after the distribution in the equation. The expression should have the distributed terms fully and properly combined.
### Correct Simplified Expression
So, the correct final simplified expression is:
\[
8 \cos^2 \beta - 4
\]
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