Verify the identity. (Simplify at each step.) 3 cos² B-3 sin² ß = 3 - 6 sin² ß 3 cos² B-3 sin² B = (3- || X - 3 sin² ß = 3 - 6 sin² ß
Verify the identity. (Simplify at each step.) 3 cos² B-3 sin² ß = 3 - 6 sin² ß 3 cos² B-3 sin² B = (3- || X - 3 sin² ß = 3 - 6 sin² ß
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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![**Verify the identity. (Simplify at each step)**
The given identity to verify is:
\[ 3 \cos^2 \beta - 3 \sin^2 \beta = 3 - 6 \sin^2 \beta \]
**Step-by-Step Simplification:**
1. **Start with the left-hand side:**
\[ 3 \cos^2 \beta - 3 \sin^2 \beta \]
2. **Factor out the common term "3":**
\[ 3 (\cos^2 \beta - \sin^2 \beta) \]
(Note: In the problem image, a blue box follows this step, indicating where the next term should be filled, but contains a red 'X' suggesting a mistake or incomplete step in the provided solution.)
3. **Compare it with the right-hand side:**
\[ 3 - 6 \sin^2 \beta \]
At this stage, there appears to be an error pointed out (red 'X') in the verification step shown in the image.
Given the current identity setup and simplification steps, the user must accurately fill in the missing steps to ensure that both sides of the equation match.
The steps should correct or fully simplify any discrepancy effectively.
This transcription should guide students to ensuring every factor and simplification is accurately followed to verify mathematical identities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2F05512573-b9d8-4fcd-98b5-3a33319643c7%2Fczw7afm_processed.png&w=3840&q=75)
Transcribed Image Text:**Verify the identity. (Simplify at each step)**
The given identity to verify is:
\[ 3 \cos^2 \beta - 3 \sin^2 \beta = 3 - 6 \sin^2 \beta \]
**Step-by-Step Simplification:**
1. **Start with the left-hand side:**
\[ 3 \cos^2 \beta - 3 \sin^2 \beta \]
2. **Factor out the common term "3":**
\[ 3 (\cos^2 \beta - \sin^2 \beta) \]
(Note: In the problem image, a blue box follows this step, indicating where the next term should be filled, but contains a red 'X' suggesting a mistake or incomplete step in the provided solution.)
3. **Compare it with the right-hand side:**
\[ 3 - 6 \sin^2 \beta \]
At this stage, there appears to be an error pointed out (red 'X') in the verification step shown in the image.
Given the current identity setup and simplification steps, the user must accurately fill in the missing steps to ensure that both sides of the equation match.
The steps should correct or fully simplify any discrepancy effectively.
This transcription should guide students to ensuring every factor and simplification is accurately followed to verify mathematical identities.
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