Prove the following identity. cos“ e = 1 cos 20 + cos? 20 2 4 We begin by using a Double-Angle Formula twice on the right side of the equation. We can then expand all products and add the fractions to simplify. cos 20 cos? 20 2 1 (2 cos? e – 1)2 4 2 4 cos4 e – 4 cos? e + 1 4 4 cos4 e 4 = cos e II

Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter1: The Six Trigonometric Functions
Section1.5: More On Identities
Problem 100PS
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Prove the following identity.
cos“ e =
1
cos 20
+
cos? 20
2
4
We begin by using a Double-Angle Formula twice on the right side of the equation. We can then expand all products and add the fractions to simplify.
cos 20
cos? 20
2
1
(2 cos? e – 1)2
4
2
4 cos4 e – 4 cos? e + 1
4
4
cos4 e
4
= cos e
II
Transcribed Image Text:Prove the following identity. cos“ e = 1 cos 20 + cos? 20 2 4 We begin by using a Double-Angle Formula twice on the right side of the equation. We can then expand all products and add the fractions to simplify. cos 20 cos? 20 2 1 (2 cos? e – 1)2 4 2 4 cos4 e – 4 cos? e + 1 4 4 cos4 e 4 = cos e II
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