Prove that the following identity is true. 1. 2 csc? x 1+ cos X 1- cos x 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
CoS X
+
cos? x
en Shot
1...7.59 PM
1
1
+
1 + cos x
- COS X
1 -
1 -
(1 – cos x) + (1 + cos x)
1 -
en Shot
L...8.07 PM
=
1 -
en Shot
1..8.27 PM
2
= 2 csc? x
en Shot"
Transcribed Image Text:ck
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
CoS X
+
cos? x
en Shot
1...7.59 PM
1
1
+
1 + cos x
- COS X
1 -
1 -
(1 – cos x) + (1 + cos x)
1 -
en Shot
L...8.07 PM
=
1 -
en Shot
1..8.27 PM
2
= 2 csc? x
en Shot
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