Establish the identity. sec ² (-0)-1 = tan ²0 Which of the following four statements establishes the identity? A. ec ² (-0)-1=1+(- tan 0)² = 1 + tan ²0 = tan ²0 B. sec ec²(-0)-1 = (sec 0)² - 1 = sec - 1 = sec ²0+1 = tan ²0 OC. sec ² (-0)-1 = - sec ² (-0) + 1 = sec ²0 -1 = tan ²0 O D. sec ² (-0)- 1 = (sec 0)² - 1 = sec ²0 -1 = tan ²0
Establish the identity. sec ² (-0)-1 = tan ²0 Which of the following four statements establishes the identity? A. ec ² (-0)-1=1+(- tan 0)² = 1 + tan ²0 = tan ²0 B. sec ec²(-0)-1 = (sec 0)² - 1 = sec - 1 = sec ²0+1 = tan ²0 OC. sec ² (-0)-1 = - sec ² (-0) + 1 = sec ²0 -1 = tan ²0 O D. sec ² (-0)- 1 = (sec 0)² - 1 = sec ²0 -1 = tan ²0
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Establish the Identity
#### Identity:
\[
\sec^2(-\theta) - 1 = \tan^2 \theta
\]
#### Problem:
Which of the following four statements establishes the identity?
#### Options:
**A.**
\[
\sec^2(-\theta) - 1 = 1 + (-\tan \theta)^2 = 1 + \tan^2 \theta = \tan^2 \theta
\]
**B.**
\[
\sec^2(-\theta) - 1 = (\sec \theta)^2 - 1 = \sec^2 \theta + 1 = \tan^2 \theta
\]
**C.**
\[
\sec^2(-\theta) - 1 = -\sec^2(-\theta) + 1 = \sec^2 \theta - 1 = \tan^2 \theta
\]
**D.**
\[
\sec^2(-\theta) - 1 = (\sec \theta)^2 - 1 = \sec^2 \theta - 1 = \tan^2 \theta
\]
The text presents a trigonometric identity problem requiring the establishment of the identity \(\sec^2(-\theta) - 1 = \tan^2 \theta\). Four options are given, each presenting a different sequence of steps or transformations to verify this identity. The correct choice will demonstrate the equivalence of the given expression and the target trigonometric identity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96d7e99a-c3dd-47c1-87ff-8a4c1e4775a5%2F8c88af39-face-4999-b38e-0f3b4d0b4411%2F8juy0vh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Establish the Identity
#### Identity:
\[
\sec^2(-\theta) - 1 = \tan^2 \theta
\]
#### Problem:
Which of the following four statements establishes the identity?
#### Options:
**A.**
\[
\sec^2(-\theta) - 1 = 1 + (-\tan \theta)^2 = 1 + \tan^2 \theta = \tan^2 \theta
\]
**B.**
\[
\sec^2(-\theta) - 1 = (\sec \theta)^2 - 1 = \sec^2 \theta + 1 = \tan^2 \theta
\]
**C.**
\[
\sec^2(-\theta) - 1 = -\sec^2(-\theta) + 1 = \sec^2 \theta - 1 = \tan^2 \theta
\]
**D.**
\[
\sec^2(-\theta) - 1 = (\sec \theta)^2 - 1 = \sec^2 \theta - 1 = \tan^2 \theta
\]
The text presents a trigonometric identity problem requiring the establishment of the identity \(\sec^2(-\theta) - 1 = \tan^2 \theta\). Four options are given, each presenting a different sequence of steps or transformations to verify this identity. The correct choice will demonstrate the equivalence of the given expression and the target trigonometric identity.
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