4 tan 0+ tan? e-3 14) 3 cot* 0+11 cot? 0 – 4 15) 3 csc? 0 - 4 sec? 0
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
Complete simplify each problem so that no quotient is in the answer.
![### Mathematical Expressions:
#### Expression 14:
\[
\frac{4 \tan^4 \theta + \tan^2 \theta - 3}{\sec^2 \theta}
\]
- This expression involves the tangent (\(\tan\)) and secant (\(\sec\)) trigonometric functions.
- In the numerator, \(4 \tan^4 \theta + \tan^2 \theta - 3\) includes a term with \(\tan^4\) (tangent raised to the fourth power) and a quadratic term in \(\tan^2\).
- The denominator is \(\sec^2 \theta\), or the square of the secant function.
#### Expression 15:
\[
\frac{3 \cot^4 \theta + 11 \cot^2 \theta - 4}{3 \csc^2 \theta - 4}
\]
- This expression involves the cotangent (\(\cot\)) and cosecant (\(\csc\)) trigonometric functions.
- In the numerator, \(3 \cot^4 \theta + 11 \cot^2 \theta - 4\) has a fourth power term of cotangent and a quadratic term in \(\cot^2\).
- The denominator is \(3 \csc^2 \theta - 4\), including a term \(\csc^2\) (cosecant squared) and a constant.
These expressions can be used to explore identities and transformations involving trigonometric functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd9448c9-9639-4279-8a27-332e65606234%2Fd7b7fd58-8367-4d7c-9a1d-bc686e751c30%2F6ufdvbf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Mathematical Expressions:
#### Expression 14:
\[
\frac{4 \tan^4 \theta + \tan^2 \theta - 3}{\sec^2 \theta}
\]
- This expression involves the tangent (\(\tan\)) and secant (\(\sec\)) trigonometric functions.
- In the numerator, \(4 \tan^4 \theta + \tan^2 \theta - 3\) includes a term with \(\tan^4\) (tangent raised to the fourth power) and a quadratic term in \(\tan^2\).
- The denominator is \(\sec^2 \theta\), or the square of the secant function.
#### Expression 15:
\[
\frac{3 \cot^4 \theta + 11 \cot^2 \theta - 4}{3 \csc^2 \theta - 4}
\]
- This expression involves the cotangent (\(\cot\)) and cosecant (\(\csc\)) trigonometric functions.
- In the numerator, \(3 \cot^4 \theta + 11 \cot^2 \theta - 4\) has a fourth power term of cotangent and a quadratic term in \(\cot^2\).
- The denominator is \(3 \csc^2 \theta - 4\), including a term \(\csc^2\) (cosecant squared) and a constant.
These expressions can be used to explore identities and transformations involving trigonometric functions.
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