In 7.2 problem 10 since the half angle identity of cos^2 is being applied to cos^4 shouldn't the half angle identity be squared?

Calculus: Early Transcendentals
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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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In 7.2 problem 10 since the half angle identity of cos^2 is being applied to cos^4 shouldn't the half angle identity be squared? 

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Yes, the half angle identity of cos2t must be squared while applying to cos4t.

The correct calculation of the integral is as follows.

Calculus homework question answer, step 1, image 1

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