Question
The period of the function |sinx|+|cosx| is
Answer: Option A
:
A
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
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:
A
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
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