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a b с с d 1 + tan²8 tan²0-1 1 + cot²0 cot²0-1

a b с с d 1 + tan²8 tan²0-1 1 + cot²0 cot²0-1

Trigonometry (11th Edition)
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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**Trigonometric Identity Question** **Question:** Which of the following identities is equal to \(\sec^2 \theta\)? **Explanation:** This problem requires understanding of trigonometric identities, specifically those involving the secant function. The secant function is directly related to the cosine function. Recall the Pythagorean identity: \[ \sec^2 \theta = 1 + \tan^2 \theta \] To solve this, one must identify the correct trigonometric identity among the given options that matches \(\sec^2 \theta\). The correct expression that is equal to \(\sec^2 \theta\) typically simplifies to \( 1 + \tan^2 \theta \). Make sure you are familiar with basic trigonometric identities to approach this problem effectively. Understanding and memorizing the fundamental identities will greatly aid in solving such problems. **Note:** If there were multiple-choice options provided, they would typically be analyzed and the correct identity selected, confirming the understanding of the trigonometric relationships.
Transcribed Image Text:**Trigonometric Identity Question** **Question:** Which of the following identities is equal to \(\sec^2 \theta\)? **Explanation:** This problem requires understanding of trigonometric identities, specifically those involving the secant function. The secant function is directly related to the cosine function. Recall the Pythagorean identity: \[ \sec^2 \theta = 1 + \tan^2 \theta \] To solve this, one must identify the correct trigonometric identity among the given options that matches \(\sec^2 \theta\). The correct expression that is equal to \(\sec^2 \theta\) typically simplifies to \( 1 + \tan^2 \theta \). Make sure you are familiar with basic trigonometric identities to approach this problem effectively. Understanding and memorizing the fundamental identities will greatly aid in solving such problems. **Note:** If there were multiple-choice options provided, they would typically be analyzed and the correct identity selected, confirming the understanding of the trigonometric relationships.
The provided image contains a list of four trigonometric expressions labeled a through d. These expressions involve tangent (tan) and cotangent (cot) functions of the angle θ. Here is a transcription of the content: a) \( 1 + \tan^2 \theta \) b) \( \tan^2 \theta - 1 \) c) \( 1 + \cot^2 \theta \) d) \( \cot^2 \theta - 1 \) These expressions are frequently encountered in trigonometry, particularly in relation to trigonometric identities and equations. The tangent and cotangent functions are related to the sine and cosine functions, and these expressions can often be simplified or rephrased using fundamental trigonometric identities. For instance, the identity \( 1 + \tan^2 \theta = \sec^2 \theta \) is one such example that relates these expressions to the secant function.
Transcribed Image Text:The provided image contains a list of four trigonometric expressions labeled a through d. These expressions involve tangent (tan) and cotangent (cot) functions of the angle θ. Here is a transcription of the content: a) \( 1 + \tan^2 \theta \) b) \( \tan^2 \theta - 1 \) c) \( 1 + \cot^2 \theta \) d) \( \cot^2 \theta - 1 \) These expressions are frequently encountered in trigonometry, particularly in relation to trigonometric identities and equations. The tangent and cotangent functions are related to the sine and cosine functions, and these expressions can often be simplified or rephrased using fundamental trigonometric identities. For instance, the identity \( 1 + \tan^2 \theta = \sec^2 \theta \) is one such example that relates these expressions to the secant function.
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