Prove the identity. 2 tan(x) 1+ tan?(x) sin(2x)

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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**Mathematical Identity Proof**

**Problem Statement:**

Prove the identity:

\[
\frac{2 \cdot \tan(x)}{1 + \tan^2(x)} = \sin(2x)
\]

**Response Field:**

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**Grading Information:**

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**Support Section:**

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**Description:**

The task is to prove the given trigonometric identity. 

**Components Explanation:**

- **Equation:** You are required to show mathematically that the left side \(\frac{2 \cdot \tan(x)}{1 + \tan^2(x)}\) is equal to the right side \(\sin(2x)\).

- **User Input Box:** Space to write out the mathematical steps and justification for proving the identity.

- **Need Help Section:** An option is provided for supplemental guidance, indicated by “Need Help?” with a “Read It” button for additional resources or hints.
Transcribed Image Text:**Mathematical Identity Proof** **Problem Statement:** Prove the identity: \[ \frac{2 \cdot \tan(x)}{1 + \tan^2(x)} = \sin(2x) \] **Response Field:** [Empty input box for student response] **Grading Information:** This answer has not been graded yet. **Support Section:** Need Help? [Read It Button] **Description:** The task is to prove the given trigonometric identity. **Components Explanation:** - **Equation:** You are required to show mathematically that the left side \(\frac{2 \cdot \tan(x)}{1 + \tan^2(x)}\) is equal to the right side \(\sin(2x)\). - **User Input Box:** Space to write out the mathematical steps and justification for proving the identity. - **Need Help Section:** An option is provided for supplemental guidance, indicated by “Need Help?” with a “Read It” button for additional resources or hints.
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