Prove that the following identity is true. 1 1 = 2 csc2 x 1 cos X 1 cos X We begin on the left side of the equation by writing the two fractions with common denominators, and add. We can then use a Pythagorean Identity to simplify the denominator. Lastly, we use a Reciprocal Identity to remove the fraction 1 cos X 1 - cos X 1 1 1 cos X 1 cos2 x 1 1 - cos X (1 cos x) + (1 + cos x) 1 - 2 1 2 = 2 csc2 x
Prove that the following identity is true. 1 1 = 2 csc2 x 1 cos X 1 cos X We begin on the left side of the equation by writing the two fractions with common denominators, and add. We can then use a Pythagorean Identity to simplify the denominator. Lastly, we use a Reciprocal Identity to remove the fraction 1 cos X 1 - cos X 1 1 1 cos X 1 cos2 x 1 1 - cos X (1 cos x) + (1 + cos x) 1 - 2 1 2 = 2 csc2 x
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 that the following identity is true.
1
1
= 2 csc2 x
1 cos X
1 cos X
We begin on the left side of the equation by writing the two fractions with common denominators, and add. We can then use a Pythagorean Identity to simplify the denominator. Lastly,
we use a Reciprocal Identity to remove the fraction
1 cos X
1 - cos X
1
1
1 cos X
1 cos2 x
1
1 - cos X
(1 cos x) + (1 + cos x)
1 -
2
1
2
= 2 csc2 x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07855119-4567-46b4-87d0-bc5ee906db91%2F98ccb5a6-b805-445a-9d22-ee16e19a770c%2Fin6xcrn.png&w=3840&q=75)
Transcribed Image Text:Prove that the following identity is true.
1
1
= 2 csc2 x
1 cos X
1 cos X
We begin on the left side of the equation by writing the two fractions with common denominators, and add. We can then use a Pythagorean Identity to simplify the denominator. Lastly,
we use a Reciprocal Identity to remove the fraction
1 cos X
1 - cos X
1
1
1 cos X
1 cos2 x
1
1 - cos X
(1 cos x) + (1 + cos x)
1 -
2
1
2
= 2 csc2 x
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