Prove that the following identity is true. tan 8 - cot e = sin² e – cos² e sin e cos e We begin by separating the right side of the equation into two fractions. We can then reduce and use the Ratio Identities to simplify. sin? e – cos² e sin 8 cos e cos? e sin 8 cos e sin 8 cos e cos e sin e cos e = tan 8 - cot e

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 69E
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Prove that the following identity is true.
sin? e - cos? e
sin e cos 0
tan 8 - cot e =
We begin by separating the right side of the equation into two fractions. We can then reduce and use the Ratio Identities to simplify.
sin? e - cos? e
cos? e
sin e cos e
sin 8 cos e
sin e cos e
cos e
sin 6
cos e
= tan 6 - cot e
Transcribed Image Text:Prove that the following identity is true. sin? e - cos? e sin e cos 0 tan 8 - cot e = We begin by separating the right side of the equation into two fractions. We can then reduce and use the Ratio Identities to simplify. sin? e - cos? e cos? e sin e cos e sin 8 cos e sin e cos e cos e sin 6 cos e = tan 6 - cot e
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tanθ - cotθ = sin2θ - cos2θsinθcosθ

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