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63. First, observe sin 4x = 2 sin 2x cos 2x = 2 sin 2.x(1 – 2 sin? x) = 2 sin 2x – 4 sin 2x sin² x = 2 sin 2x – 8 sin³ x cos x. Then »(12x – 8 sin 2x + sin 4.x) + C = x - sin 2x – i sin³ x cos x + C = x - sin x cos x – (- sin' x cos x + C.

63. First, observe sin 4x = 2 sin 2x cos 2x = 2 sin 2.x(1 – 2 sin? x) = 2 sin 2x – 4 sin 2x sin² x = 2 sin 2x – 8 sin³ x cos x. Then »(12x – 8 sin 2x + sin 4.x) + C = x - sin 2x – i sin³ x cos x + C = x - sin x cos x – (- sin' x cos x + C.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.5: Product-to-sum And Sum-to-product Formulas
Problem 2E
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63. First, observe sin 4x = 2 sin 2x cos 2x = 2 sin 2.x(1 – 2 sin? x) = 2 sin 2x – 4 sin 2x sin² x = 2 sin 2x – 8 sin³ x cos x. Then »(12x – 8 sin 2x + sin 4.x) + C = x - sin 2x – i sin³ x cos x + C = x - sin x cos x – (- sin' x cos x + C.
Transcribed Image Text:63. First, observe sin 4x = 2 sin 2x cos 2x = 2 sin 2.x(1 – 2 sin? x) = 2 sin 2x – 4 sin 2x sin² x = 2 sin 2x – 8 sin³ x cos x. Then »(12x – 8 sin 2x + sin 4.x) + C = x - sin 2x – i sin³ x cos x + C = x - sin x cos x – (- sin' x cos x + C.
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