The period of the function
`f(x)=||sinx|-|cosx||` , is

Options

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

Answer

A

Explanation

We have,
`f(pi//2+x)=||sin(pi//2+x)|-|cos(pi//2)+x)||`
` implies f(pi//2+x=||cosx|-|sinx||`
`implies f(pi//2+x)=||sinx|-|cosx||`
`implies f(pi//2+x)=f(x) ` for all ` x in R `.
Hence , f(x) is periodic with period `pi//2`.
Students are advised to learn the periods of following standard functions.