Verify the identity. cos(u) sec(u) = cot(u) tan(u) Use a Reciprocal Identity to rewrite the expression, and then simplify. cos(u) sec(u) = (cos(u) cos(u) sec(u)) tan(u) tan(u) X cos(u). 1 cos(u) tan (u) = ) = X X
Verify the identity. cos(u) sec(u) = cot(u) tan(u) Use a Reciprocal Identity to rewrite the expression, and then simplify. cos(u) sec(u) = (cos(u) cos(u) sec(u)) tan(u) tan(u) X cos(u). 1 cos(u) tan (u) = ) = X X
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
![**Verifying the Trigonometric Identity**
Given Identity:
\[ \frac{\cos(u) \sec(u)}{\tan(u)} = \cot(u) \]
**Step-by-Step Verification:**
1. **Use a Reciprocal Identity to Rewrite the Expression**
\[ \frac{\cos(u) \sec(u)}{\tan(u)} \]
**Rewrite using reciprocal identities:**
\[ \cos(u) \sec(u) = 1 \]
(since sec(u) = \(\frac{1}{\cos(u)}\), therefore \(\cos(u) \cdot \frac{1}{\cos(u)} = 1\))
Therefore,
\[ \frac{1}{\tan(u)} \]
2. **Simplify the Expression**
\[ \frac{1}{\tan(u)} = \cot(u) \]
Therefore, we have verified the given identity.
\[ \boxed{\frac{\cos(u) \sec(u)}{\tan(u)} = \cot(u)} \]
In the image, there were some incorrect steps indicated by red crosses. The process went wrong when trying to cross-multiply by \(\tan(u)\) unnecessarily. The correct approach is to directly simplify using reciprocal identities as shown above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6841f1bf-ebcf-44b9-bde6-b1a56299f544%2Fbca70d2a-9553-4ed2-8c2f-93693c53711a%2F47k2dzz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Verifying the Trigonometric Identity**
Given Identity:
\[ \frac{\cos(u) \sec(u)}{\tan(u)} = \cot(u) \]
**Step-by-Step Verification:**
1. **Use a Reciprocal Identity to Rewrite the Expression**
\[ \frac{\cos(u) \sec(u)}{\tan(u)} \]
**Rewrite using reciprocal identities:**
\[ \cos(u) \sec(u) = 1 \]
(since sec(u) = \(\frac{1}{\cos(u)}\), therefore \(\cos(u) \cdot \frac{1}{\cos(u)} = 1\))
Therefore,
\[ \frac{1}{\tan(u)} \]
2. **Simplify the Expression**
\[ \frac{1}{\tan(u)} = \cot(u) \]
Therefore, we have verified the given identity.
\[ \boxed{\frac{\cos(u) \sec(u)}{\tan(u)} = \cot(u)} \]
In the image, there were some incorrect steps indicated by red crosses. The process went wrong when trying to cross-multiply by \(\tan(u)\) unnecessarily. The correct approach is to directly simplify using reciprocal identities as shown above.
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 2 steps with 2 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