Show that the following statement is an identity by transforming the left side into the right side. (1 - cos e)(1 + cos e) = sin? e We begin by performing the multiplication on the left side. We can then use the Pythagorean Identity to simplify. (1 - cos 0)(1 + cos 0) = 1 - = sin? e Because we have succeeded in transforming the left side into the right side, we have shown that the statement (1 - cos e)(1 + cos e) = sin² e is an identity. + X - S

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 66E
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Show that the following statement is an identity by transforming the left side into the right side.
Operations
(1 - cos 0)(1 + cos e) = sin2 e
Functions
We begin by performing the multiplication on the left side. We can then use the Pythagorean Identity to simplify.
Symbols
Relations
(1 - cos 0)(1 + cos e) = 1 -
Sets
o!
Vectors
= sin? e
Trig
Because we have succeeded in transforming the left side into the right side, we have shown that the statement (1 - cos 0)(1 + cos 0) = sin? e is an identity.
Greek
Transcribed Image Text:Show that the following statement is an identity by transforming the left side into the right side. Operations (1 - cos 0)(1 + cos e) = sin2 e Functions We begin by performing the multiplication on the left side. We can then use the Pythagorean Identity to simplify. Symbols Relations (1 - cos 0)(1 + cos e) = 1 - Sets o! Vectors = sin? e Trig Because we have succeeded in transforming the left side into the right side, we have shown that the statement (1 - cos 0)(1 + cos 0) = sin? e is an identity. Greek
We begin by writing the left side in terms of sin e and cos e. We can then simplify the two compound fractions separately, and use the Pythagorean Ide
sin e
cos e
+
sec e
sin e
cos e
csc e
1/cos e
= cos? e +
= 1
cos e
sin e
= 1 is an identity.
csc e
Because we have succeeded in transforming the left side into the right side, we have shown that the statement
sec e
Transcribed Image Text:We begin by writing the left side in terms of sin e and cos e. We can then simplify the two compound fractions separately, and use the Pythagorean Ide sin e cos e + sec e sin e cos e csc e 1/cos e = cos? e + = 1 cos e sin e = 1 is an identity. csc e Because we have succeeded in transforming the left side into the right side, we have shown that the statement sec e
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