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The period of the function $f (x) = \frac{| \sin x | - | \cos x |}{| \sin x + \cos x |} is$

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π2

2π

None of these

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detailed solution

Correct option is C

We have,f(π+x)=|sin⁡(π+x)|−|cos⁡(π+x)||sin⁡(π+x)+cos⁡(π+x)|=|sin⁡x|−|cos⁡x||sin⁡x+cos⁡x|=f(x) for all x∴ f (x) is periodic with period π.

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The period of the function f(x)=|sin⁡x|−|cos⁡x||sin⁡x+cos⁡x| is

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The period of the function $f (x) = \frac{| \sin x | - | \cos x |}{| \sin x + \cos x |} is$