Final answer:
In the sentence, 'Whatever you tell me will remain our secret', the noun clause 'Whatever you tell me' functions as the subject of the sentence because it is performing the action of remaining a secret.
Step-by-step explanation:
In the given sentence, 'Whatever you tell me' is a noun clause. A noun clause is a group of words that serves the same purpose as a noun. The noun clause here acts as a subject because it performs the action in the sentence. The action being 'will remain our secret'. Therefore, we can say 'Whatever you tell me' is the subject of this sentence because it's the thing doing the action of remaining a secret.
Learn more about Noun Clauses