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f of x= cosine of (x) minus sine of (4x).
We check and see if it is a periodic function. We examine f of (x plus w pi).
equals cosine
of (x plus 2 pi) minus sine of (4 times (x+2 pi)) =
cosine of (x plus 2 pi) minus sine
of
(4x+
8 pi)).
Since cosine is a periodic function and the period is 2 pi,
we have cosine of (2x),
minus,
sine is also a periodic function, and the period is 2 pi, 8 pi is a
multiple of 2 pi,
so, we have
sine of (4x). It is the same as f of x.
And 2 pi is the smallest number such that f of (x + this number) = f of x.
So, we conclude that the period is 2 pi.