А теперь нечто совершенно иное

unit Unit1;

{$mode objfpc}{$H+}

interface

uses
  Classes, SysUtils, Forms, Controls, Graphics, Dialogs, StdCtrls, math;


type

  { TForm1 }

  TForm1 = class(TForm)
    Button1: TButton;
    Edit1: TEdit;
    Edit2: TEdit;
    Label1: TLabel;
    StaticText1: TStaticText;
    StaticText2: TStaticText;
    procedure Button1Click(Sender: TObject);
    procedure FormCreate(Sender: TObject);
  private

  public

  end;

var
  Form1: TForm1;

implementation

{$R *.lfm}

{ TForm1 }

procedure TForm1.Button1Click(Sender: TObject);
var
x, i, EPS: real;
a, a1: real;
begin
     x:=strtofloat (Edit1.Text);
     EPS:=strtofloat (Edit2.Text);
     if EPS < 0 then
     halt;
     a := x;
        a1 := 0;
         i := 2;
         while abs(a - a1) > EPS do begin
               a1 := a;
            a := 2 + (1/(EPS**i))* cos(a1 - 2*x)**2;
            i += 1;
         end;
    Label1.Caption:=floattostr(a);
end;

procedure TForm1.FormCreate(Sender: TObject);
begin

end;

end.