Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 69E
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Show that the following statement is an identity by transforming the left side into the right side.
cos e cot e + sin e = csc e
We begin by writing the left side in terms of sin e and cos e. We can then combine terms as a single fraction, simplify and rewrite in terms of csc e.
cos e cot e + sin e = (cos e) ·
+ sin e
sin e
cos? 0 +
sin e
= csc e
Because we have succeeded in transforming the left side into the right side, we have shown that the statement cos e cot e + sin e = csc e is an identity.
Transcribed Image Text:Show that the following statement is an identity by transforming the left side into the right side. cos e cot e + sin e = csc e We begin by writing the left side in terms of sin e and cos e. We can then combine terms as a single fraction, simplify and rewrite in terms of csc e. cos e cot e + sin e = (cos e) · + sin e sin e cos? 0 + sin e = csc e Because we have succeeded in transforming the left side into the right side, we have shown that the statement cos e cot e + sin e = csc e is an identity.
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