Maxima:Products and sums of trigonometric terms

I have an expression which can be  either  a product of trigonometric terms 
or a sum of trigonometric terms, for example: expr = z1*z2 or expr = z1 + z2.

(1) Is there a Maxima command that indicates whether expr is a product of 
terms or a sum of terms ?

(2) In applying the built-in Maxima simplification functions trigsimp, 
trigreduce, trigrat, etc on products of terms, it seems that the map function 
has to be used to obtain the desired simplification (example below). 

Is there perhaps another approach ?

Thanks very much.

C. Frangos.



%i271) z1;

(%o271) cos(q2)*sin(q4)+sin(q2)*cos(q4)
(%i272) z2;

(%o272) sin(q6+q5)*cos(q8)
(%i273) trigsimp(z1*z2);

(%o273) (cos(q2)*sin(q4)+sin(q2)*cos(q4))*sin(q6+q5)*cos(q8)
(%i274) trigrat(z1*z2);

(%o274) -(cos(q8+q6+q5+q4+q2)-cos(q8+q6+q5-q4-q2)-cos(q8-q6-q5+q4+q2)
                             +cos(q8-q6-q5-q4-q2))
         /4
(%i275) trigreduce(z1*z2);

(%o275) (cos(q8+q6+q5-q4-q2)-cos(q8+q6+q5+q4+q2))/4
         +(cos(q8-q6-q5+q4+q2)-cos(q8-q6-q5-q4-q2))/4
(%i276) map(trigreduce,z1*z2);

(%o276) sin(q4+q2)*sin(q6+q5)*cos(q8)
(%i277) map(trigrat,z1*z2);

(%o277) sin(q4+q2)*sin(q6+q5)*cos(q8)
(%i278) map(trigsimp,z1*z2);

(%o278) (cos(q2)*sin(q4)+sin(q2)*cos(q4))*sin(q6+q5)*cos(q8)
(%i279)