Prove the identity. 5 tan(3x) = 15 tan(x) – 5 tan²(x) 1- 3 tan?(x) Rewrite 3x as 2x + x and use the Addition Formula for Tangent to simplify. 5 tan(3x) = 5 tan(2x + x) 1- tan(2x) tan(x) Use the Double-Angle Formula for Tangent to simplify. + 5 tan(x) ctan(x)) 19 + 10 tan(x) (1 – tan (x)) – Need Help? Read It Watch It
Prove the identity. 5 tan(3x) = 15 tan(x) – 5 tan²(x) 1- 3 tan?(x) Rewrite 3x as 2x + x and use the Addition Formula for Tangent to simplify. 5 tan(3x) = 5 tan(2x + x) 1- tan(2x) tan(x) Use the Double-Angle Formula for Tangent to simplify. + 5 tan(x) ctan(x)) 19 + 10 tan(x) (1 – tan (x)) – Need Help? Read It Watch It
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
Could you please write the questions clearly and understandably? Thank you.
![**Prove the identity.**
\[ 5 \tan(3x) = \frac{15 \tan(x) - 5 \tan^3(x)}{1 - 3 \tan^2(x)} \]
Rewrite \(3x\) as \(2x + x\) and use the Addition Formula for Tangent to simplify.
\[ 5 \tan(3x) = 5 \left( \frac{\tan(2x + x)}{1 - \tan(2x) \tan(x)} \right) \]
Use the Double-Angle Formula for Tangent to simplify.
\[ = \frac{\_ \ + \ 5 \tan(x)}{1 - \left( \_ \right)\tan(x)} \]
\[ = \frac{\_ \ + 10 \tan(x)}{(1 - \tan^2(x)) \_} \]
\[ = \_ \]
**Need Help?**
Buttons: [Read It] [Watch It]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3bcaea97-3c57-4685-8473-33f5b83e373d%2Fd4c74ad0-2b5f-4583-b825-75f373aa074e%2F5wp3co_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Prove the identity.**
\[ 5 \tan(3x) = \frac{15 \tan(x) - 5 \tan^3(x)}{1 - 3 \tan^2(x)} \]
Rewrite \(3x\) as \(2x + x\) and use the Addition Formula for Tangent to simplify.
\[ 5 \tan(3x) = 5 \left( \frac{\tan(2x + x)}{1 - \tan(2x) \tan(x)} \right) \]
Use the Double-Angle Formula for Tangent to simplify.
\[ = \frac{\_ \ + \ 5 \tan(x)}{1 - \left( \_ \right)\tan(x)} \]
\[ = \frac{\_ \ + 10 \tan(x)}{(1 - \tan^2(x)) \_} \]
\[ = \_ \]
**Need Help?**
Buttons: [Read It] [Watch It]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning