Final answer:
A trial balance that is "in balance" simply proves that the total debits equal the total credits, demonstrating the equality of the two in the accounting records.
Step-by-step explanation:
A trial balance that is "in balance" proves d) The equality of the debits and credits. This means that the total debits equal the total credits in the ledger accounts. It is important to note, however, that while a balanced trial balance indicates that the accounting equation is balanced, it does not guarantee that all transactions have been recorded correctly or that the journal entries have been properly posted to the ledger.
To ensure more accuracy and validity in the accounting records, other measures need to be taken. These include reviewing journal entries for accuracy, reconciling bank statements, and reviewing ledgers for proper classification of transactions.