Is the following indentity true? ### Trigonometric Identity VerificationConsider the following identity:\[ \sec^4(\theta) - \tan^4(\theta) = \frac{1 + \sin^2(\theta)}{\cos^2(\theta)} \]**Objective:** Determine if this identity is true.**Explanation:**1. **Left Hand Side (LHS):** - $\sec(\theta) = \frac{1}{\cos(\theta)}$ - $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ - Therefore, $\sec^4(\theta) = \left(\frac{1}{\cos(\theta)}\right)^4 = \frac{1}{\cos^4(\theta)}$ - And $\tan^4(\theta) = \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^4 = \frac{\sin^4(\theta)}{\cos^4(\theta)}$ - Thus, LHS becomes: \[ \frac{1}{\cos^4(\theta)} - \frac{\sin^4(\theta)}{\cos^4(\theta)} = \frac{1 - \sin^4(\theta)}{\cos^4(\theta)} \]2. **Right Hand Side (RHS):** - $\frac{1 + \sin^2(\theta)}{\cos^2(\theta)}$**Conclusion:**The identity reduces to comparing:\[ \frac{1 - \sin^4(\theta)}{\cos^4(\theta)} \quad \text{and} \quad \frac{1 + \sin^2(\theta)}{\cos^2(\theta)} \]To determine if they are indeed equal, further simplification or manipulation might be required.

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Description: Is the following indentity true? ### Trigonometric Identity VerificationConsider the following identity:\[ \sec^4(\theta) - \tan^4(\theta) = \frac{1 + \sin^2(\theta)}{\cos^2(\theta)} \]**Objective:** Determine if this identity is true.**Explanation:*

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Math

Trigonometry

Is the following indentity true? sec (6)-tan (0) = 1+sin? (e) cos?(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°.

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