The peroid of the function `f(x) =(|sinx|-|cosx|)/(|sin x + cosx|)` is

Options

A. `(pi)/(2)`
B. `2pi`
C. `pi `
D. none of these

Answer

C

Explanation

We observe that
`f(x+pi)=(|sin (pi+x)|-|cos(pi+x)|)/(|sin(pi x - cos x)|+cos(x+pi)|)`
`rArr f(x +pi)=(|sin x|-|cosx|)/(|-sin x - cosx|)=(|sin x|-|cosx|)/(|sin x + cos x)|`
`rArr f(x + pi)= f(x) "for all " x in R`
Therefore , `f(x)` is periodic with period `pi`.