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The period of the function f(x)=|sinx...

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

A

`pi//2`

B

`pi`

C

`2pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
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`.
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