reserve x,x1,x2,x3 for Real;

theorem
  cos(x)<>0 implies tan(2*x)=(2*tan(x))/(1-(tan(x))^2)
proof
  assume
A1: cos(x)<>0;
  tan(2*x) = tan(x+x) .=(tan(x)+tan(x))/(1-tan(x)*tan(x)) by A1,SIN_COS4:7
    .=(2*tan(x))/(1-tan(x)*tan(x));
  hence thesis;
end;
