Rewrite the following expression in terms of the given function. tan x + cot x sec X tan x + cot x sec x CSC X
Rewrite the following expression in terms of the given function. tan x + cot x sec X tan x + cot x sec x CSC 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
![### Rewrite the following expression in terms of the given function.
\[ \frac{\tan x + \cot x}{\sec x} ; \quad \csc x \]
\[ \frac{\tan x + \cot x}{\sec x} = \boxed{\phantom{answer}} \]
---
In this exercise, you are asked to rewrite the given trigonometric expression \(\frac{\tan x + \cot x}{\sec x}\) in terms of \(\csc x\) and simplify it. This involves using trigonometric identities. To get the correct answer, you need to follow these steps:
1. Recall the definitions and relationships among the trigonometric functions:
- \(\tan x = \frac{\sin x}{\cos x}\)
- \(\cot x = \frac{\cos x}{\sin x}\)
- \(\sec x = \frac{1}{\cos x}\)
- \(\csc x = \frac{1}{\sin x}\)
2. Substitute these definitions into the original expression.
3. Simplify the resulting expression using algebraic manipulations and trigonometric identities.
Feel free to use this knowledge to work through the problem to find how to express the given function properly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ff184a1-2c1e-42c2-8527-d6b5d9856587%2Fbda5a97b-b32d-406d-934f-bd492fd6c3a3%2Frqhp5pl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Rewrite the following expression in terms of the given function.
\[ \frac{\tan x + \cot x}{\sec x} ; \quad \csc x \]
\[ \frac{\tan x + \cot x}{\sec x} = \boxed{\phantom{answer}} \]
---
In this exercise, you are asked to rewrite the given trigonometric expression \(\frac{\tan x + \cot x}{\sec x}\) in terms of \(\csc x\) and simplify it. This involves using trigonometric identities. To get the correct answer, you need to follow these steps:
1. Recall the definitions and relationships among the trigonometric functions:
- \(\tan x = \frac{\sin x}{\cos x}\)
- \(\cot x = \frac{\cos x}{\sin x}\)
- \(\sec x = \frac{1}{\cos x}\)
- \(\csc x = \frac{1}{\sin x}\)
2. Substitute these definitions into the original expression.
3. Simplify the resulting expression using algebraic manipulations and trigonometric identities.
Feel free to use this knowledge to work through the problem to find how to express the given function properly.
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