Question: Trigonometric expression manipulation

Hello,

In a mechanical problem, i have to deal with a system with trigonometric expression. The variables are gamma[1](t), psi[1](t), phi[1](t), alpha(t), beta(t), x(t). The orthers are parameters.

I would like to have a explicit relations between  gamma[1](t), psi[1](t), phi[1](t) and alpha(t), beta(t), x(t).

In orthers words, i would like to have 

alpha(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

beta(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

 x(t) = f( gamma[1](t), psi[1](t), phi[1](t)).

Of course, the expresions of alpha(t), beta(t), and x(t) should be complex. Nevertheless, it will avoid me to have to solve Newton Raphson algorithm to solve these constraints equations.

Normally, it should be feasible.

When i have only one equation and not a system, isolate function is helpful.

But in this case, i don't manage to have my relations.

Have you some ideas to expression these relations ?

alpha(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

beta(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

 x(t) = f( gamma[1](t), psi[1](t), phi[1](t)).

Here the code of the equations :

restart:
with(LinearAlgebra):
with(Student[MultivariateCalculus]):
with(plots):
constants:= ({constants} minus {gamma})[]:
`evalf/gamma`:= proc() end proc:
`evalf/constant/gamma`:= proc() end proc:
unprotect(gamma);
restart:
with(LinearAlgebra):
with(Student[MultivariateCalculus]):
with(plots):
constants:= ({constants} minus {gamma})[]:
`evalf/gamma`:= proc() end proc:
`evalf/constant/gamma`:= proc() end proc:
unprotect(gamma);
eq_liai[1]:= rF[1]*cos(a[1])-cos(a[1])*cos(gamma[1](t))*e[1]-l[1]*(cos(phi[1](t))*cos(a[1])*cos(gamma[1](t))*cos(psi[1](t))-cos(phi[1](t))*cos(a[1])*sin(gamma[1](t))*sin(psi[1](t))-sin(a[1])*sin(phi[1](t)))-cos(alpha(t))*rBTP[1]*cos(a[1])-sin(alpha(t))*sin(beta(t))*rBTP[1]*sin(a[1])-sin(alpha(t))*cos(beta(t))*h = 0;
eq_liai[2]:= rF[1]*sin(a[1])-sin(a[1])*cos(gamma[1](t))*e[1]-l[1]*(cos(phi[1](t))*sin(a[1])*cos(gamma[1](t))*cos(psi[1](t))-cos(phi[1](t))*sin(a[1])*sin(gamma[1](t))*sin(psi[1](t))+cos(a[1])*sin(phi[1](t)))-cos(beta(t))*rBTP[1]*sin(a[1])+sin(beta(t))*h = 0;
eq_liai[3] := h[1]+sin(gamma[1](t))*e[1]+l[1]*(sin(gamma[1](t))*cos(psi[1](t))+cos(gamma[1](t))*sin(psi[1](t)))*cos(phi[1](t))+sin(alpha(t))*rBTP[1]*cos(a[1])-cos(alpha(t))*sin(beta(t))*rBTP[1]*sin(a[1])-cos(alpha(t))*cos(beta(t))*h-z(t) = 0;

or directly a maple file

constraints.mw

Thanks a lot for your help