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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
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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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 \(\cot 2x = \frac{1}{\tan 2x}\).
Transcribed Image Text:### 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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