Replacement of a group of variables in trigonometric expression

Question

I would like to make simplification of trigonometric expressions by using a replacement a group of variables.

Here the equation I have to simplify :

   -Cos[γ[1][t] - θ[1][t] - ψ[1][t]] l[f] + 
  m[f] Sin[γ[1][t]] + 
  c[f] Sin[γ[1][t] - θ[1][t]] - 
  h[f] Sin[γ[1][t] - θ[1][t] - ψ[1][t]] + 
  x[P1][
   t] == -Cos[γ[2][t] - θ[2][t] - ψ[2][t]] l[f] + 
  m[f] Sin[γ[2][t]] + 
  c[f] Sin[γ[2][t] - θ[2][t]] - 
  h[f] Sin[γ[2][t] - θ[2][t] - ψ[2][t]] + 
  x[P2][t]

For the simplification I also this equation

γ[1][t] - θ[1][t] - ψ[1][t] == γ[2][t] - θ[2][t] - ψ[2][t]

Consequently, I would like to replace only in the right hand side the group of variables γ[2][t] - θ[2][t] - ψ[2][t] by γ[1][t] - θ[1][t] - ψ[1][t]

After simplifications, I would like to obtain this equation :

m[f] Sin[γ[1][t]] + c[f] Sin[γ[1][t] - θ[1][t]] + x[P1][t] == 
  m[f] Sin[γ[2][t]] + c[f] Sin[γ[2][t] - θ[2][t]] + x[P2][t]

Have you some ideas so to do this replacement γ[1][t] - θ[1][t] - ψ[1][t] == γ[2][t] - θ[2][t] - ψ[2][t] in the right hand side of my equation ?

Answer 1

try this:

FullSimplify[
   -Cos[γ[1][t] - θ[1][t] - ψ[1][t]] l[f] + m[f] Sin[γ[1][t]] + 
   c[f] Sin[γ[1][t] - θ[1][t]] - h[f] Sin[γ[1][t] - θ[1][t] - ψ[1][t]] + 
   x[P1][t] == (-Cos[γ[2][t] - θ[2][t] - ψ[2][t]] l[f] + m[f] Sin[γ[2][t]] + 
   c[f] Sin[γ[2][t] - θ[2][t]] - h[f] Sin[γ[2][t] - θ[2][t] - ψ[2][t]] + 
   x[P2][t]) /. (γ[2][t] - θ[2][t] - ψ[2][t]) -> (γ[1][t] - θ[1][t] - ψ[1][t])
]