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Question
Hi,
I've been trying to figure this out...how do i prove this identity?
sin x cos^3 x - cos x sin^3 x = 1/4 sin 4x
Questioner: Britney
Category: Advanced Math
Subject: proving identities
Question: Hi, I've been trying to figure this out...how do i prove this identity? sin x cos^3 x - cos x sin^3 x = 1/4 sin 4x
..................................
Hi, Britney,
I am very disappointed that you didn't send this one to me. Well, anyway, using my normal notation, S = sin x, C = cos x:
Remembering that sin(2A) = 2 sin A cos A, and that
cos^2(x) - sin^2(x) = cos(2x), we can do the following:
SC^3 - CS^3 = SC(C^2 - S^2) = 1/2 sin(2x)cos(2x) = 1/2 (1/2 sin(4x)) = 1/4 sin(4x)
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Questioner's Rating
| Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |
| Comment | well thank you...you bailed me out again. i didn't send it to you because i didn't want to bother you again. but thank you very much...your the best. | ||
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Advanced Math
Answers by Expert:
Paul Klarreich
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I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.
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I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.
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