reserve x,x1,x2,x3 for Real;

theorem
  sin(x)<>0 implies cot(2*x)=((cot(x))^2-1)/(2*cot(x))
proof
  assume
A1: sin(x)<>0;
  cot(2*x)=cot(x+x) .=(cot(x)*cot(x)-1)/(cot(x)+cot(x)) by A1,SIN_COS4:9
    .=(cot(x)*cot(x)-1)/(2*cot(x));
  hence thesis;
end;
