This is optional however i want to understand how to answer so can you show the steps ### Trigonometric Identities and Equations**Problem 4:** Given the identity $\cos 2x = \cos^2 x - \sin^2 x$ (Optional).#### Part (a)**Objective:** Verify $\sin 2x = 2 \sin x \cos x$.#### Part (b)**Objective:** Express $\cot 2x$ in terms of $\cot x$.*Hint:* Consider $\cot 2x = \frac{\cos 2x}{\sin 2x}$.#### Part (c)**Objective:** Verify your result in (b) using $\tan 2x = \frac{2 \tan x}{1 - \tan^2 x}$.*Hint:* Consider $\cot 2x = \frac{1}{\tan 2x}$.

Answered: Image /qna-images/answer/b5d70a20-71c7-477a-bf21-951559b032cd.jpg

4. Given cos 2x = cos²x - sin² x. (Optional) (a) Verify sin 2x = 2 sin x cosx. cos 2x, (b) Express cot 2x in terms of cotx. (hint. Consider cot 2x = sin 2x (c) Verify your result in (b) using tan 2x = 2 tan x 1-tan² x (hint. Consider cot 2x tan 2x

4. Given cos 2x = cos²x - sin² x. (Optional) (a) Verify sin 2x = 2 sin x cosx. cos 2x, (b) Express cot 2x in terms of cotx. (hint. Consider cot 2x = sin 2x (c) Verify your result in (b) using tan 2x = 2 tan x 1-tan² x (hint. Consider cot 2x tan 2x

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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Question

This is optional however i want to understand how to answer so can you show the steps

### Trigonometric Identities and Equations

**Problem 4:** Given the identity $\cos 2x = \cos^2 x - \sin^2 x$ (Optional).

#### Part (a)
**Objective:** Verify $\sin 2x = 2 \sin x \cos x$.

#### Part (b)
**Objective:** Express $\cot 2x$ in terms of $\cot x$.
*Hint:* Consider $\cot 2x = \frac{\cos 2x}{\sin 2x}$.

#### Part (c)
**Objective:** Verify your result in (b) using $\tan 2x = \frac{2 \tan x}{1 - \tan^2 x}$.
*Hint:* Consider $\cot 2x = \frac{1}{\tan 2x}$.

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