Please consider the following sentence with a particular emphasis on the determiner, the:
Have you locked the door and the cellar?
Could you please advice novices (like myself) whether the usage of the for the second object (i.e. cellar) above should be deemed redundant or not? Resulting in:
Have you locked the door and cellar?
In the sentence you have used, the second "the" is a bit redundant.
If the two items you are referring to are closely related, then don't use the second "the." For example:
"The key and lock"
"The girl and boy"
If you are trying to show difference between the two objects, then most likely you should use both "the"s. For example:
"The big cat and the small cat"
"The open door and the closed door"
In most cases, it does not sound too bad if you use both of the "The"s, so do not feel too pressured to say it a certain way.
