WITH CHECK ADD CONSTRAINT followed by CHECK CONSTRAINT vs. ADD CONSTRAINT

To demonstrate how this works--

CREATE TABLE T1 (ID INT NOT NULL, SomeVal CHAR(1));
ALTER TABLE T1 ADD CONSTRAINT [PK_ID] PRIMARY KEY CLUSTERED (ID);

CREATE TABLE T2 (FKID INT, SomeOtherVal CHAR(2));

INSERT T1 (ID, SomeVal) SELECT 1, 'A';
INSERT T1 (ID, SomeVal) SELECT 2, 'B';

INSERT T2 (FKID, SomeOtherVal) SELECT 1, 'A1';
INSERT T2 (FKID, SomeOtherVal) SELECT 1, 'A2';
INSERT T2 (FKID, SomeOtherVal) SELECT 2, 'B1';
INSERT T2 (FKID, SomeOtherVal) SELECT 2, 'B2';
INSERT T2 (FKID, SomeOtherVal) SELECT 3, 'C1';  --orphan
INSERT T2 (FKID, SomeOtherVal) SELECT 3, 'C2';  --orphan

--Add the FK CONSTRAINT will fail because of existing orphaned records
ALTER TABLE T2 ADD CONSTRAINT FK_T2_T1 FOREIGN KEY (FKID) REFERENCES T1 (ID);   --fails

--Same as ADD above, but explicitly states the intent to CHECK the FK values before creating the CONSTRAINT
ALTER TABLE T2 WITH CHECK ADD CONSTRAINT FK_T2_T1 FOREIGN KEY (FKID) REFERENCES T1 (ID);    --fails

--Add the CONSTRAINT without checking existing values
ALTER TABLE T2 WITH NOCHECK ADD CONSTRAINT FK_T2_T1 FOREIGN KEY (FKID) REFERENCES T1 (ID);  --succeeds
ALTER TABLE T2 CHECK CONSTRAINT FK_T2_T1;   --succeeds since the CONSTRAINT is attributed as NOCHECK

--Attempt to enable CONSTRAINT fails due to orphans
ALTER TABLE T2 WITH CHECK CHECK CONSTRAINT FK_T2_T1;    --fails

--Remove orphans
DELETE FROM T2 WHERE FKID NOT IN (SELECT ID FROM T1);

--Enabling the CONSTRAINT succeeds
ALTER TABLE T2 WITH CHECK CHECK CONSTRAINT FK_T2_T1;    --succeeds; orphans removed

--Clean up
DROP TABLE T2;
DROP TABLE T1;

Further to the above excellent comments about trusted constraints:

select * from sys.foreign_keys where is_not_trusted = 1 ;
select * from sys.check_constraints where is_not_trusted = 1 ;

An untrusted constraint, much as its name suggests, cannot be trusted to accurately represent the state of the data in the table right now. It can, however, but can be trusted to check data added and modified in the future.

Additionally, untrusted constraints are disregarded by the query optimiser.

The code to enable check constraints and foreign key constraints is pretty bad, with three meanings of the word "check".

ALTER TABLE [Production].[ProductCostHistory] 
WITH CHECK -- This means "Check the existing data in the table".
CHECK CONSTRAINT -- This means "enable the check or foreign key constraint".
[FK_ProductCostHistory_Product_ProductID] -- The name of the check or foreign key constraint, or "ALL".

The first syntax is redundant - the WITH CHECK is default for new constraints, and the constraint is turned on by default as well.

This syntax is generated by the SQL management studio when generating sql scripts -- I'm assuming it's some sort of extra redundancy, possibly to ensure the constraint is enabled even if the default constraint behavior for a table is changed.