Period of mod cotx+ mod cosx+ mod tanx+ mod sinx is?

HI,
|sinx| has period π and |cosx| has period π so is for the rest 

This is an even function and sinx, cosx are complementary.

Hence, |sinx| +|cosx| has period = 1/2 (LCM of π,π ) = π/2

Thus, period of |sinx| + |cosx| is π/2.
similarly for |tanx| +|cotx| has period = 1/2 (LCM of π,π ) = π/2
So over all period = LCM of  π/2

 and  π/2=  π/2

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