Question: Simplification of trigonometric equations. V

Hello,

I would like to simplify a trigonometric equation that I obtain with a vectorial closure (in mechanics)

Here the equation that I would like to simplify 

eq_liaison := (-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*l2[1]+((-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*cos(th(t))+(-cos(p(t)+g(t))*cos(a(t))+sin(a(t))*sin(b(t))*sin(p(t)+g(t)))*sin(th(t)))*l3[1]+(-sin(a(t))*sin(g(t))*sin(b(t))+cos(a(t))*cos(g(t)))*xb[1]+sin(a(t))*cos(b(t))*yb[1]+(sin(a(t))*sin(b(t))*cos(g(t))+cos(a(t))*sin(g(t)))*zb[1]+x(t)-xp(t) = 0

Do you have ideas so as to simplify again this expression ?

This expression can still be simplified. You can find here the result expected :

I find surprising that I have so many difficulties to make trigonometric simplications with the trigonometric functions.

I attached the code 

Download TrigoTransformVectorialEquations.mwTrigoTransformVectorialEquations.mw

Thank you for your help