Recall the Pythagorean identity which states that 1 + tan² u = sec² u. Using this Pythagorean identity, simplify the denominator. -14 -14 (sec² x - 1) X
Recall the Pythagorean identity which states that 1 + tan² u = sec² u. Using this Pythagorean identity, simplify the denominator. -14 -14 (sec² x - 1) 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°.
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![### Pythagorean Identity Simplification: An Example
#### Recall the Pythagorean identity which states that:
\(1 + \tan^2 u = \sec^2 u.\)
#### Using this Pythagorean identity, simplify the denominator:
The given expression:
\[
\frac{-14}{\sec^2 x - 1} = \frac{-14}{}
\]
The denominator in the expression,
\[
\sec^2 x - 1
\]
should be simplified using the Pythagorean identity. The identity helps to transform \(\sec^2 x - 1\) into another trigonometric term.
Notice the red cross mark next to the blank box indicating an incorrect attempt to simplify the denominator.
To simplify correctly:
\[
\sec^2 x - 1 = \tan^2 x
\]
Thus, the simplified form of the given expression should be:
\[
\frac{-14}{\tan^2 x}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2Fa0e4dcfd-58b8-44e6-899f-2f20fa896757%2Fl39nmyu_processed.png&w=3840&q=75)
Transcribed Image Text:### Pythagorean Identity Simplification: An Example
#### Recall the Pythagorean identity which states that:
\(1 + \tan^2 u = \sec^2 u.\)
#### Using this Pythagorean identity, simplify the denominator:
The given expression:
\[
\frac{-14}{\sec^2 x - 1} = \frac{-14}{}
\]
The denominator in the expression,
\[
\sec^2 x - 1
\]
should be simplified using the Pythagorean identity. The identity helps to transform \(\sec^2 x - 1\) into another trigonometric term.
Notice the red cross mark next to the blank box indicating an incorrect attempt to simplify the denominator.
To simplify correctly:
\[
\sec^2 x - 1 = \tan^2 x
\]
Thus, the simplified form of the given expression should be:
\[
\frac{-14}{\tan^2 x}
\]
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