f(x)=[2cos^2(x/2)-1]+sinx
=cosx+sinx
=√2sin(x+π/4)
∵x∈R ∴x+π/4∈R
∵f(x)=sinx∈(-1,1)
∴f(x)=√2sin(x+π/4)∈(-√2,√2)
T=2π/1=2π