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Question

The period of the function |sinx|+|cosx| is

A
π2
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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 A π2
The smallest of π2,2π,4π,π is π2
Let f(x)=|sin x|+|cos x|.
f(x+π2)=sin(x+π2)+cos(x+π2)
=|cos x|+|sin x|
=|cos x|+|sin x|
=f (x)
The period of given function is π2

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