Show that the familiar identities cos 3 x = 3/4 cos x + 1/4 cos 3x and

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Show that the familiar identities cos3 x = 3/4 cos x + 1/4 cos 3x and sinx = 3/4 sin x -1/4 sin 3x can be interpreted as Fourier series expansions. Develop cos4 x.

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