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Which of the following is an equivalent expression to sin - (sin )(cos²0)? O cos²e O cos³e O sin²e O sin³e

Which of the following is an equivalent expression to sin - (sin )(cos²0)? O cos²e O cos³e O sin²e O sin³e

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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**Question:** Which of the following is an equivalent expression to \( \sin \theta - (\sin \theta / \cos^2 \theta) \)? **Options:** - ○ \( \cos \theta \) - ○ \( \cos^3 \theta \) - ○ \( \sin^2 \theta \) - ○ \( \sin^3 \theta \)
Transcribed Image Text:**Question:** Which of the following is an equivalent expression to \( \sin \theta - (\sin \theta / \cos^2 \theta) \)? **Options:** - ○ \( \cos \theta \) - ○ \( \cos^3 \theta \) - ○ \( \sin^2 \theta \) - ○ \( \sin^3 \theta \)
Expert Solution
Step 1

Given expression      sin(θ)-(sin(θ))(cos2(θ))

Here we use the following identity:             

 

 

                                       Sin2(θ)+cos2(θ)=1⇒ sin2(θ)=1-cos2(θ)

 

   Now    sin(θ)-(sin(θ))(cos2(θ))

 

         ⇒  sin(θ)[1-cos^2(θ)]

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