Using the expansions of cos (3x - x) and cos (3x + x), prove that

1/2 (cos 2x - cos 4x) ≡ sin 3x sin x.

Question

Kianna Hutchinson

Mathematics

7 March, 11:51

Using the expansions of cos (3x - x) and cos (3x + x), prove that

1/2 (cos 2x - cos 4x) ≡ sin 3x sin x.

+3

Answers (1)

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Kailyn Riggs · Answer 1

Cos (A - B) = cos A cos B + sin A sin B

cos (A + B) = cos A cos B - sin A sin B

cos 2x = cos (3x - x) = cos 3x cos x + sin 3x sin x

cos 4x = cos (3x + x) = cos 3x cos x - sin 3x sin x

1/2 (cos 2x - cos 4x) = 1/2 (cos 3x cos x + sin 3x sin x - cos 3x cos x + sin 3x sin x) = 1/2 (2 sin 3x sin x) = sin 3x sin x.

Using the expansions of cos (3x - x) and cos (3x + x), prove that1/2 (cos 2x - cos 4x) ≡ sin 3x sin x.

Using the expansions of cos (3x - x) and cos (3x + x), prove that

1/2 (cos 2x - cos 4x) ≡ sin 3x sin x.