Question: How to simplify that?

Hello,

I have two equations (1) and (2) and i want to divide (2) with (3). A good point is that Maple understand division with equations. Nevertheless, I didn't obtain a simplified solution.

Here my code :

restart;
eq1:=-sin(alpha0(t))*cos(beta0(t)) = -sin(alpha[1](t))*cos(beta[1](t));
-sin(alpha0(t)) cos(beta0(t)) = -sin(alpha[1](t)) cos(beta[1](t))
eq2:=cos(alpha0(t))*cos(beta0(t)) = cos(alpha[1](t))*cos(beta[1](t));
cos(alpha0(t)) cos(beta0(t)) = cos(alpha[1](t)) cos(beta[1](t))
simplify(eq1/eq2,trig);

Here the result obtained :-sin(alpha0(t))/cos(alpha0(t)) = -sin(alpha[1](t))/cos(alpha[1](t))

Consequently, I would like to obtain tan(alpha0(t))=tan(alpha1(t))

Do you have ideas why I didn't obtain a simplified result ? And How can I obtain the solution with tangents ?

Thank you for your help