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$f (x) = \frac{\cos x}{[\frac{2 x}{π}] + \frac{1}{2}},$ where x is not an integral multiple of $π$ and [ ] denotes the greatest integer function is

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Correct option is A

fx=cos−x−2xπ+12=cosx−1−2xπ+12(as x is not an integral multiple of π)⇒f−x=−cosx2xπ+12=−f(x)⇒f(x) is an odd function

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fx=cosx2xπ+12, where x is not an integral multiple of π and [ ] denotes the greatest integer function is

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$f (x) = \frac{\cos x}{[\frac{2 x}{π}] + \frac{1}{2}},$ where x is not an integral multiple of $π$ and [ ] denotes the greatest integer function is