Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than one correct form of each answer.) 3 sec³(x) - 3 sec²(x) - 3 sec(x) + 3 2 3 tan (x) (sec (x) - 1) Your answer cannot be understood or graded. More Information
Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than one correct form of each answer.) 3 sec³(x) - 3 sec²(x) - 3 sec(x) + 3 2 3 tan (x) (sec (x) - 1) Your answer cannot be understood or graded. More Information
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.1: Verifying Trigonometric Identities
Problem 67E
Related questions
Question
![### Understanding and Factoring Trigonometric Expressions
#### Example Problem:
**Task**: Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than one correct form of each answer.)
Expression:
\[ 3 \sec^3(x) - 3 \sec^2(x) - 3 \sec(x) + 3 \]
**Incorrect Attempt**:
\[ 3 \tan^2(x) (\sec(x) - 1) \]
This answer could not be understood or graded. For more assistance and details, click on "More Information".
#### Fundamental Identities to Remember:
1. \(\sec(x) = \frac{1}{\cos(x)}\)
2. \(\tan(x) = \frac{\sin(x)}{\cos(x)}\)
3. \(\tan^2(x) + 1 = \sec^2(x)\)
These identities can often simplify and help in factoring trigonometric expressions appropriately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2Fca3b8e08-a051-4970-a116-27674ef31984%2Fek4sc4_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding and Factoring Trigonometric Expressions
#### Example Problem:
**Task**: Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than one correct form of each answer.)
Expression:
\[ 3 \sec^3(x) - 3 \sec^2(x) - 3 \sec(x) + 3 \]
**Incorrect Attempt**:
\[ 3 \tan^2(x) (\sec(x) - 1) \]
This answer could not be understood or graded. For more assistance and details, click on "More Information".
#### Fundamental Identities to Remember:
1. \(\sec(x) = \frac{1}{\cos(x)}\)
2. \(\tan(x) = \frac{\sin(x)}{\cos(x)}\)
3. \(\tan^2(x) + 1 = \sec^2(x)\)
These identities can often simplify and help in factoring trigonometric expressions appropriately.
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