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B
2π
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C
4π
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D
π
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Solution
The correct option is Aπ2 The smallest of π2,2π,4π,π is π2 Let f(x)=|sinx|+|cosx|. ∴f(x+π2)=∣∣sin(x+π2)∣∣+∣∣cos(x+π2)∣∣ =|cosx|+|−sinx| =|cosx|+|sinx| =f (x) ∴The period of given function is π2