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

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

A

`pi`

B

`(pi)/(2)`

C

`2pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=|sin x |+| cos x|`.
We know that | sin x| and | cos x| are periodic with period `pi`.
Therefore, f(x) should be periodic with period `pi.`
But , `| sin(pi//2+x)|= | cos x| and | cox(pi//2)|=| sin x|` .
Therefore , by Result III, f(x) is periodic with period `pi//2`.
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