Question

The period of the function
`f(x)=|sinx|-|cosx|` , is
A. `pi//2`
B. `pi`
C. `2pi`
D. none of these

Answer 1

Correct Answer - B
We have,
`f(x)=|sinx)-|cos x|`
`:. f(pi+x)=|sin(pi+x)|-|cos(pi+x)|`
`implies f(pi+x)=| -sinx|-|-cos x|`
`implies f(pi+x)=|sin x|-|cosx|=f(x)` for all ` x in R `
` implies f(pi+x)=f(x)` for all ` x in R `
So, f(x) is periodic with period `pi`.