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Amiraneli [1.4K]
4 years ago
9

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

Mathematics
1 answer:
Rus_ich [418]4 years ago
5 0
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.
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