-/8 Points] DETAILS MY NOTES AUFCAT7 6.1.009. Verify the identity. COS X secx+tan x ASK YOUR TEACHER 1 - sin x Working with the left-hand side, multiply the numerator and denominator by the conjugate of the denominator, and find the product in the denominator. (Simplify at each step.) cos x(1 + sin x) cos x 1 - sin x == - (1 sin x) = cos x(1 + sin x) Then, use the Pythagorean Identity for cos² x, and simplify by dividing out the common factors. (Simplify at each step.) LHS = cos x(1 + sin x) (1 + sin x) = Finally, rewrite the fraction as two fractions, and then use a Reciprocal Identity and a Ratio Identity to simplify. (Simplify at each step.) 1 sin x LHS = +
-/8 Points] DETAILS MY NOTES AUFCAT7 6.1.009. Verify the identity. COS X secx+tan x ASK YOUR TEACHER 1 - sin x Working with the left-hand side, multiply the numerator and denominator by the conjugate of the denominator, and find the product in the denominator. (Simplify at each step.) cos x(1 + sin x) cos x 1 - sin x == - (1 sin x) = cos x(1 + sin x) Then, use the Pythagorean Identity for cos² x, and simplify by dividing out the common factors. (Simplify at each step.) LHS = cos x(1 + sin x) (1 + sin x) = Finally, rewrite the fraction as two fractions, and then use a Reciprocal Identity and a Ratio Identity to simplify. (Simplify at each step.) 1 sin x LHS = +
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 14RE
Related questions
Question
![-/8 Points]
DETAILS
MY NOTES
AUFCAT7 6.1.009.
Verify the identity.
COS X
secx+tan x
ASK YOUR TEACHER
1 - sin x
Working with the left-hand side, multiply the numerator and denominator by the conjugate of the denominator, and find the product
in the denominator. (Simplify at each step.)
cos x(1 + sin x)
cos x
1 - sin x
==
-
(1 sin x)
=
cos x(1 + sin x)
Then, use the Pythagorean Identity for cos² x, and simplify by dividing out the common factors. (Simplify at each step.)
LHS =
cos x(1 + sin x)
(1 + sin x)
=
Finally, rewrite the fraction as two fractions, and then use a Reciprocal Identity and a Ratio Identity to simplify. (Simplify at each
step.)
1
sin x
LHS =
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3667b1b4-dc94-45e1-8d51-eb9a6807d5ae%2F0aa6c870-1b3f-41db-980e-ce31f652603b%2Fqo3njjd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:-/8 Points]
DETAILS
MY NOTES
AUFCAT7 6.1.009.
Verify the identity.
COS X
secx+tan x
ASK YOUR TEACHER
1 - sin x
Working with the left-hand side, multiply the numerator and denominator by the conjugate of the denominator, and find the product
in the denominator. (Simplify at each step.)
cos x(1 + sin x)
cos x
1 - sin x
==
-
(1 sin x)
=
cos x(1 + sin x)
Then, use the Pythagorean Identity for cos² x, and simplify by dividing out the common factors. (Simplify at each step.)
LHS =
cos x(1 + sin x)
(1 + sin x)
=
Finally, rewrite the fraction as two fractions, and then use a Reciprocal Identity and a Ratio Identity to simplify. (Simplify at each
step.)
1
sin x
LHS =
+
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