Clear["`*"];
fi[r_,θ_]:=1/(l!)*(k*r*Cos[θ])^l;
T1[η_]:=1;
T2[η_]:=η/3;
f[η_,r_,θ_]:=T1[η]*fi[r,θ];
v[η_,r_,θ_]:=T2[η]*fi[r,θ];
Hs=2/ηs;
Ho=2/ηo;
l=1;

vo =D[v[ηo,r,θ],r]/.r->0;
vs = D[v[ηs,r,θ],r];
κ=2*Integrate[((r-(ηo-η))/(2*r*(ηo-η)))(Cot[θ]*D[f[η,ηo-η,θ],θ]+D[f[η,ηo-η,θ],{θ,2}]),{η,ηo,ηs}]/.ηs->ηo-r;
ϵ=(f[ηo,0,θ]-f[ηs,r,θ])-(vo-vs)+2*Integrate[D[f[η,ηo-η,θ],η],{η,ηo,ηs}]/.ηs->ηo-r;
γ=(2/r)Integrate[f[η,ηo-η,θ],{η,ηo,ηs}]/.ηs->ηo-r;
RSD = (1/Hs)(-D[f[ηs,r,θ],ηs]-D[vs,r])/.ηs->ηo-r;
Simplify[vo]
Simplify[vs]
Simplify[κ]
Simplify[ϵ]
Simplify[γ]
Simplify[RSD]

Δevo=Hs*v[ηs,r,θ]-ϵ/.{ηs->ηo-r};
Δm=-f[ηs,r,θ]+(1-(1/(r*Hs)))ϵ+vo+κ+γ/.{ηs->ηo-r};
Δn=-3f[ηs,r,θ]+3Hs*v[ηs,r,θ]+2*vo-(((D[Hs,ηs])/(Hs^2))+(2/(r*Hs)))*ϵ+2κ+2γ+RSD/.{ηs->ηo-r};
Devo = Δevo*l!;
Dm = Δm*l!;
Dn= Δn*l!;
Collect[TrigExpand[Δevo/.{θ->ArcCos[x]}],x]/.{x->Cos[θ]}
Collect[TrigExpand[Δm/.{θ->ArcCos[x]}],x]/.{x->Cos[θ]}
Collect[TrigExpand[Δn/.{θ->ArcCos[x]}],x]/.{x->Cos[θ]}