Question

what is period of |sinx|+|cosx|

Answer 1

Now the question is asking about the period of the function then you know that f(x+T) = f(x) then the smallest value of T is the principal period of the function.From the equation only you may get the answer as π/2
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Second approach can be that you know that period of |sinx| and |cosx| is π and so the period of their sum function is π only but π is the period but not the fundamental period of function Hence check for smaller values of T satisfying the equation and that is π/2 only so the period is π/2.
Hope that it is clear to youyou otherwise refer to the function chapter of any mathematics book you will get the answer.

Answer 2

Answer:

Step-by-step explanation:

|sin x| has a period of π.|cos x| has also a period of π.

Period of |sin x|+|cos x| will be the LCM of the two periods of the functions.

Hence, period is π.But, these are even complementary functions so it is a case of exception.

Period becomes π÷2.

Hope you understood