y=2+sin(x/2)-sinx
=2+(1-cosx)/2-sinx
=-[sinx+(1/2)cosx]+(5/2)
=-(√5)/2sin(x+φ)+(5/2)
∵x∈R
∴ymax=(√5)/2+(5/2)=(2+√5)/2 y=2+sin(x/2)-sinx
=2+(1-cosx)/2-sinx
=-[sinx+(1/2)cosx]+(5/2)
=-(√5)/2sin(x+φ)+(5/2)
∵x∈R
∴ymax=(√5)/2+(5/2)=(2+√5)/2