a problem of substitution with a rule

Question

I would to make this substitution with 2 rules. Nothing is happening.

     (Sin[η2] ((Cos[θ2]* Cos[ψ1])/Sin[ψ1] + 
       Cos[ψ2] Sin[θ2]) == Cos[η2] Sin[ψ2]) /. 
  Sin[ψ1] -> (Cos[ϕ2] Sin[η2])/Sin[ψ2] /. 
 Cos[ψ1] -> Cos[η2] Cos[θ2] Cos[ϕ2] - 
   Sin[θ2] Sin[ϕ2]

Have you an idea why i didn't manage to make these substitutions ? Sorry if my question is may be very simple, but i blocked.

Answer 1

Use HoldForm to stop Mathematica from simplifying,

SC = HoldForm[(Sin[\[Eta]2] ((Cos[\[Theta]2]*Cos[\[Psi]1])/
        Sin[\[Psi]1] + Cos[\[Psi]2] Sin[\[Theta]2]) == 
    Cos[\[Eta]2] Sin[\[Psi]2])]

SC /. Sin[\[Psi]1] -> (Cos[\[Phi]2] Sin[\[Eta]2])/Sin[\[Psi]2] /. 
 Cos[\[Psi]1] -> 
  Cos[\[Eta]2] Cos[\[Theta]2] Cos[\[Phi]2] - 
   Sin[\[Theta]2] Sin[\[Phi]2]