Simplify a complex trigonometric equation resulting from constraint solving

Bendesarts just a moment. 0 answers, 0 views
simplifying-expressions trigonometry

In the solving of mechanical constraints, I often meet complex trigonometric equation that I have to simplify.

Here the equation I would like to simplify :

Mathematica notebook presenting the equation

Can you help me to simplify this equation ?

I would like only cos and sin in the equation (with no more tan, Cotan or Sec functions) and gather the kinematic variables (the functions depending of time) the more possible in the cos and sin functions such as cos(gamma1(t)+psi1(t)).

Here the target that I would like to obtain (made with maple for the moment and I hope to do this with mathematica):

Target of the simplifications that I would like to obtain

Thanks a lot for your help.

P.S: I put a file attached because the equation is quiet long and have subscripts in the notation which make the equation not nice to present

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