theorem
  Z c= dom sec implies sec is_differentiable_on Z & for x st x in Z
  holds ( (sec)`|Z).x = sin.x/(cos.x)^2
proof
  assume Z c= dom sec;
  then for x st x in Z holds cos.x<>0 by RFUNCT_1:3;
  hence thesis by FDIFF_4:39;
end;
