Integrals of the form sin mx cos nx dx sin mx sin nx dx cos mx cos nx dx can be found using the following trigonometric identities sin a cos B = (sin(a – B) + sin(a + B)) sin a sin B 1 (cos(a — В) — cos(a + B)) 1 cos a cos ß ==(cos(a – B)+ cos(a + B)) Use these identities to solve the following. а. | sin(4x) cos (5x) dx b. sin(50) sin(0) de
Integrals of the form sin mx cos nx dx sin mx sin nx dx cos mx cos nx dx can be found using the following trigonometric identities sin a cos B = (sin(a – B) + sin(a + B)) sin a sin B 1 (cos(a — В) — cos(a + B)) 1 cos a cos ß ==(cos(a – B)+ cos(a + B)) Use these identities to solve the following. а. | sin(4x) cos (5x) dx b. sin(50) sin(0) de
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 70E
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Transcribed Image Text:Integrals of the form
sin mx cos nx dx
sin mx sin nx dx
cos mx cos nx dx
can be found using the following trigonometric identities
sin a cos B =
(sin(a – B) + sin(a + B))
1
sin a sin B
(cos(a — В) — cos(a + B))
2
1
cos a cos ß =¬(cos(a – B)+ cos(a + B))
Use these identities to solve the following.
а.
sin(4x) сos (5х) dx
b.
sin(50) sin(0) de
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