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Show that \sin{(3x)} = 3\sin{(x)} - 4\sin^{3}{(x)}\text{.} You will need to use five expressions in total ordered from top to bottom. Suggestion: Note that \sin{(3x)} = \sin{(x+ 2x)}\text{,} and then apply sum and double-angle formulas. (\sin{(3x)} = \sin{(x+ 2x)}\)

Show that \sin{(3x)} = 3\sin{(x)} - 4\sin^{3}{(x)}\text{.} You will need to use five expressions in total ordered from top to bottom. Suggestion: Note that \sin{(3x)} = \sin{(x+ 2x)}\text{,} and then apply sum and double-angle formulas. (\sin{(3x)} = \sin{(x+ 2x)}\)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Answer Bank sin (3x) = sin (x)(3 cos² (x) – sin² (x)) sin (3x) = sin (x) cos (2x) – cos (x) sin (2x) sin (3x) = sin (x) cos (2x) + cos (x) sin (2x) sin (3x) = sin (x)(3 – 2 sin² (x)) sin (3x) = sin (x)(-(1 – sin² (x)) – sin² (x)) sin (3x) = sin (x) sin (2x) + cos (x) cos (2x) sin (3x) = sin (x)(cos² (x) – sin² (x)) +2 sin (x) cos (x) cos (x) sin (3x) = sin (x)(- cos² (x) – sin² (x)) sin (3x) = sin (x)(cos² (x) – sin² (x)) – 2 sin (x) cos (x) cos (x) sin (3x) = 2 sin (x) sin (x) cos (x) + cos (x)(cos? (x) – sin? (x)) sin (3x) = cos (x)(cos² (x) + sin² (x)) sin (3x) = sin (x)(3(1 – sin² (x) – sin² (x)) sin (3x) = sin (x)(3 – 4 sin? (x))
Transcribed Image Text:Answer Bank sin (3x) = sin (x)(3 cos² (x) – sin² (x)) sin (3x) = sin (x) cos (2x) – cos (x) sin (2x) sin (3x) = sin (x) cos (2x) + cos (x) sin (2x) sin (3x) = sin (x)(3 – 2 sin² (x)) sin (3x) = sin (x)(-(1 – sin² (x)) – sin² (x)) sin (3x) = sin (x) sin (2x) + cos (x) cos (2x) sin (3x) = sin (x)(cos² (x) – sin² (x)) +2 sin (x) cos (x) cos (x) sin (3x) = sin (x)(- cos² (x) – sin² (x)) sin (3x) = sin (x)(cos² (x) – sin² (x)) – 2 sin (x) cos (x) cos (x) sin (3x) = 2 sin (x) sin (x) cos (x) + cos (x)(cos? (x) – sin? (x)) sin (3x) = cos (x)(cos² (x) + sin² (x)) sin (3x) = sin (x)(3(1 – sin² (x) – sin² (x)) sin (3x) = sin (x)(3 – 4 sin? (x))
Show that \sin{(3x)} = 3\sin{(x)} - 4\sin^{3}{(x)}\text{.} You will need to use five expressions in total ordered from top to bottom. Suggestion: Note that \sin{(3x)} = \sin{(x+ 2x)}\text{,} and then apply sum and double-angle formulas. (\sin{(3x)} = \sin{(x + 2x)}\) \(\sin{(3x)} = 3\sin{(x)} - 4\sin^{3}{(x)}\)
Transcribed Image Text:Show that \sin{(3x)} = 3\sin{(x)} - 4\sin^{3}{(x)}\text{.} You will need to use five expressions in total ordered from top to bottom. Suggestion: Note that \sin{(3x)} = \sin{(x+ 2x)}\text{,} and then apply sum and double-angle formulas. (\sin{(3x)} = \sin{(x + 2x)}\) \(\sin{(3x)} = 3\sin{(x)} - 4\sin^{3}{(x)}\)
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