Prove the identity. 6(tan(x) cot(x)) tan²(x) - cot²(x) Factor the denominator and then simplify. = = 6(tan(x) cot(x)) tan²(x) - cot²(x) (tan(x) + cot(x)) = II 3 sin(2x) = Use the Reciprocal Identities and simplify the compound fraction. 6(tan(x) — cot(x)) tan(x) + cot(x) cos(x) sin(x) cos(x) sin(x) + sin²(x) + cos²(x) Use a Pythagorean Identity and a Double-Angle Formula to simplify. 1

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Prove the identity.
6(tan(x) - cot(x))
tan²(x) - cot²(x)
Factor the denominator and then simplify.
6(tan(x) - cot(x))
tan²(x) - cot²(x)
= 3 sin(2x)
=
(tan(x) + cot(x))
tan(x) + cot(x)
-
6(tan(x) — cot(x))
Use the Reciprocal Identities and simplify the compound fraction.
sin(x)
cos(x)
+
cos(x)
sin(x)
sin²(x) + cos²(x)
1
Use a Pythagorean Identity and a Double-Angle Formula to simplify.
Transcribed Image Text:Prove the identity. 6(tan(x) - cot(x)) tan²(x) - cot²(x) Factor the denominator and then simplify. 6(tan(x) - cot(x)) tan²(x) - cot²(x) = 3 sin(2x) = (tan(x) + cot(x)) tan(x) + cot(x) - 6(tan(x) — cot(x)) Use the Reciprocal Identities and simplify the compound fraction. sin(x) cos(x) + cos(x) sin(x) sin²(x) + cos²(x) 1 Use a Pythagorean Identity and a Double-Angle Formula to simplify.
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