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.

Name: Is the following indentity true? ### Trigonometric Identity Verificati
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
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:*