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
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### 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.
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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