Verify the identity. 1 + cos(x) + sin(x) = 1 + sin(x) 1+ cos(x) sin(x) cos(x) 1 + cos(x) + sin(x) 1+ cos(x) sin(x) = = = = (1 + cos(x) + sin(x)) (1 + cos(x) + sin(x)) (1 + cos(x) sin(x)) (1 + cos(x) + sin(x)) + cos²(x) + sin²(x) + 2(cos(x) + sin(x) + cos(x) sin(x)) 1 + cos²(x) - sin²(x) + 2 cos(x) 2 + 2 cos(x) + 2 sin(x) + 2 sin(x) cos(x) 2 cos²(x) + 2( 1 + sin(x) cos(x) (1 + cos(x)) + sin(x) (1 + cos(x)) cos(x) (1 + ) (₁
Verify the identity. 1 + cos(x) + sin(x) = 1 + sin(x) 1+ cos(x) sin(x) cos(x) 1 + cos(x) + sin(x) 1+ cos(x) sin(x) = = = = (1 + cos(x) + sin(x)) (1 + cos(x) + sin(x)) (1 + cos(x) sin(x)) (1 + cos(x) + sin(x)) + cos²(x) + sin²(x) + 2(cos(x) + sin(x) + cos(x) sin(x)) 1 + cos²(x) - sin²(x) + 2 cos(x) 2 + 2 cos(x) + 2 sin(x) + 2 sin(x) cos(x) 2 cos²(x) + 2( 1 + sin(x) cos(x) (1 + cos(x)) + sin(x) (1 + cos(x)) cos(x) (1 + ) (₁
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 40E
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Transcribed Image Text:Verify the identity.
1 + cos(x) + sin(x)
1 + cos(x) sin(x)
1 + cos(x) + sin(x)
1 + cos(x)sin(x)
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=
=
=
=
1 + sin(x)
cos(x)
(1 + cos(x) + sin(x)) (1 + cos(x) + sin(x))
(1 + cos(x) = sin(x)) (1 + cos(x) + sin(x))
=
=
+ cos²(x) + sin²(x) + 2(cos(x) + sin(x) + cos(x) sin(x))
2 + 2 cos(x) + 2 sin(x) + 2 sin(x) cos(x)
2 cos²(x) + 2 2 ([
1 + sin(x)
cos(x)
Read It
1 + cos²(x) sin²(x) + 2 cos(x)
(1 + cos(x)) + sin(x) (1 + cos(x))
cos(x) (1 +
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