second article

In the sentence:

Please see the invoice and the(?) certificate attached.

Should we put the second the before the word certificate?

Thank you

Is this written in a letter or an email? Are the documents both physically attached to each other and actually have a physical existence? Does the recipient know of the existance of the certificate? Is it a specific certificate?

Same questions for the invoice.

That is an email, both documants are attached to it. They are not printed. Recipient knows about the existence of both and is looking forward to recieving them.

I would write, "Please see the attached invoice and the(?) certificate."

You might use "the" twice if you intended both the invoice and the certificate to be considered as separate items, i.e. not strongly linked in any way, and both to carry equal emphatic weight, e.g.

"Dear Mr Smith,
I am sorry that the paperwork we sent you was incomplete. I am now sending you the missing items. Please find attached both the invoice and the certificate."

In practise, you will find that there is usually only one the in most cases.

Ok, thank you for (the ?) explanation.