I have tested it and works fine
CREATE PROCEDURE [dbo].[Proc_Verify_Password]
@username VARCHAR(20),
@password varchar(20)
AS
BEGIN
SET NOCOUNT ON
SELECT count(*) FROM Authentication_Detail
WHERE RTRIM(LTRIM([UserName])) = RTRIM(LTRIM(@username))
AND RTRIM(LTRIM([Password])) = RTRIM(LTRIM(@password))
END