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
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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.1: Verifying Trigonometric Identities
Problem 67E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4388eea-c25e-4c1e-9a79-55ca3378b4c1%2F1c6dbf0c-199a-4feb-9008-1f3f3dbdc01a%2Fq1znwym_processed.jpeg&w=3840&q=75)
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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