Various explanations are given for the overall composition of the first five books of the old Testament. For example, the Documentary Hypothesis states the five books are a compilation of four sources: Jahwist (J), Elohist (E), Deuteronomist (D), and Priestly (P). The latest, the Deuteronomist may have developed during the reforms instituted by Josiah or possibly it was written even later in response to the exile.
Here are two passages where two different words are used together:
el and ĕlōhîm
For the LORD your God, ĕlōhîm is God, ĕlōhîm of gods, ĕlōhîm is God of gods, and Lord of lords, a great God, el a mighty, and a terrible, which regardeth not persons, nor taketh reward (Deuteronomy 10:17 KJV)
ĕlôha and ĕlōhîm
They sacrificed unto devils, not to God, ĕlôha to gods, ĕlōhîm whom they knew not, to new gods that came newly up, whom your fathers feared not. (Deuteronomy 32:17)
Furthermore, Deuteronomy has the portion of the Shema which states God, ĕlōhîm is one:
4 Hear, O Israel: The LORD our God ĕlōhîm is one LORD. 5 And thou shalt love the LORD thy God ĕlōhîm with all thine heart, and with all thy soul, and with all thy might. (Deuteronomy 6)
If Deuteronomy is written during a time of reform, or after the exile, one expects to find a text using one word to identify one God. Using three different terms to describe God is something which introduces a measure of ambiguity. This unnecessary and intentional aspect of Deuteronomy is more evident when compared with the books describing the history of this time. Neither el or ĕlôha is used in First or Second Kings. In other words, the history before, during and after Josiah's reform is described using only ĕlōhîm, as one would expect if the writer intended to convey one God.
First and Second Chronicles, both written after the exile follow Kings by using ĕlōhîm and never el. There is one instance where ĕlôha is used to identify a false god (cf. 2 Chronicles 32:15).
Obviously it is possible to accurately record the history of Israel using a single word to identify God. Yet, despite this fact, Deuteronomy unnecessarily uses three different words to identify God.
After reading the New Testament, God is revealed as physically manifesting His work through His Son and His Spirit while at the same time remaining God. With Deuteronomy in mind one could say there are two distinctly individual aspects, Son and Spirit which are singular, and another which involves Father, Son, and Spirit which is plural. The same pattern as Deuteronomy's Vorlage.
Is the Trinity, or the "tripleness" of God the best explanation for the use of el, ĕlôha, and ĕlōhîm in Deuteronomy? If not, what is a better explanation for the unnecessary and intentional uses of three different terms for God?