that the following identity is true. sec4 sec2 y - tan4 = 1 y + tan? y We begin on the left side of the equation by factoring the numerator. We can then reduce and, us Identity, simplify. sec“ y – tan“ y sec2 y - )(sec2 + tan? y) %3D sec? y + tan? y sec2 y + tan? y sec2 y - %3D = 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 49E
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Prove that the following identity is true.
sec y - tan4
sec? y + tan?
1
y
We begin on the left side of the equation by factoring the numerator. We can then reduce and, using a Pythagorean
Identity, simplify.
(sec2 + tan? y)
sec4
tan4
sec? y + tan? y
sec2
y
y -
sec? y + tan? y
sec? y -
= 1
Transcribed Image Text:Prove that the following identity is true. sec y - tan4 sec? y + tan? 1 y We begin on the left side of the equation by factoring the numerator. We can then reduce and, using a Pythagorean Identity, simplify. (sec2 + tan? y) sec4 tan4 sec? y + tan? y sec2 y y - sec? y + tan? y sec? y - = 1
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