2 cos 3x
Asked by maham237 @ in Mathematics viewed by 237 People
Using the expansions of cos(3x − x) and cos(3x + x), prove that
1/2(cos 2x − cos 4x) ≡ sin 3x sin x.
Answered by maham237 @
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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