Unsurprisingly, the Qur’an denounces explicitly the Trinity doctrine:
O People of the Book! Commit no excesses in your religion or utter anything concerning Allah but the truth. The Messiah, Jesus son of Mary, was only a messenger of Allah, His Word that He sent to Mary, and a Spirit from Him [that He sent]. So believe in Allah and His messengers, and do not say “Three.” Desist, it is better for you! Allah is one God. Far exalted is He above having offspring. His is all that is in the heavens and all that is in the earth. Allah is sufficient a disposer of affairs. (4.171) The Messiah would never scorn to be a servant to Allah, nor would the angels who are nearest to Allah. As for those who scorn His service and are arrogantly proud, He shall gather them all to Himself to answer. (4.172)
The Trinity is presented as being contrary to Jesus’ servanthood to God. The New Testament portrays Jesus as being both divine and a servant of the Divine. The Qur’an’s argument rejects this duality as an impossibility. Verse 4.171 also clearly considers the Trinity as a form of tritheism not monotheism. Put differently, the concept that God is a unity is not the same as God is one. The next verse then stresses that Jesus and the nearest angels have completely accepted their servanthood to God.
The second rejection of the doctrine of the Trinity occurs in this set of verses:
Surely they disbelieve those who say: “Allah is the Messiah son of Mary.” The Messiah himself said: “O Children of Israel! Worship Allah, my Lord and your Lord. Whoever joins other gods with Allah, for him Allah has forbidden paradise. His abode is the Fire. The evildoers shall have no helpers.” (5.72) Surely they disbelieve those who say: “Allah is one of three.” There is only one God. If they will not desist from what they say, a painful torment shall befall the disbelievers among them. (5.73) Will they not rather repent to Allah and seek His forgiveness? Allah is forgiving, merciful. (5.74) The Messiah son of Mary was no other than a messenger before whom similar messengers passed away, and his mother was a saintly woman. They used to eat food. See how We make the revelations clear to them, and see how they are deluded! (5.75) Say [O Muhammad!]: “Will you worship besides Allah that which has no power to harm or benefit you?” Allah is the Hearer, the Knower. (5.76) Say: “O People of the Book! Commit no excesses of falsehood in your religion, and do not follow the vain desires of folk of old who erred, led many astray, and strayed from the even path. (5.77) Those who disbelieved from among the Children of Israel were cursed by the tongue of David and of Jesus son of Mary. That was because they disobeyed and used to transgress. (5.78)
After rejecting the Trinity (5.73), the Qur’an goes on in verse 5.75 to stress that Jesus was only a messenger like many others who lived and died in the past, so Jesus was no special case. It also emphasizes that Mary was merely a righteous woman, in clear reference to her elevation by many Christians to divine or semi-divine status.
Some scholars have suggested that the Qur’an mistakenly takes the Trinity to be the Father, the Mother, and the Son, i.e. the divine family. This conclusion is probably influenced by the fact that in verses 5.72-75 the denouncement of deification of Mary, as well as that of Jesus, occurs after the rejection of the Trinity. I agree with Parrinder (1995: 135) that there is actually nothing in the Qur’an to suggest this interpretation. The weakness of the conclusion above becomes clear when we observe that the rejection of the Trinity in verses 4.171 is followed in verses 4.172 by the confirmation that the Messiah and the nearest angels would not scorn to be servants to God. The Qur’an could not have defined the Trinity in one verse as being God, the Messiah, and the nearest angels, and in another as God, Jesus, and Mary. The names mentioned after the Trinity are not meant to be its members.
In verse 5.116, God asks Jesus: “Did you say to people: ‘Take me and my mother for two gods besides Allah?’” This may be taken by some to mean that the Trinity is presented as consisting of God, Jesus, and Mary. But, unlike verses 4.171 and 5.73, this verse does not mention the concept of three. The Qur’an contains a large number of verses criticizing those who “take gods besides Allah,” and most of these verses have nothing to do with Jesus or the concept of the Trinity (e.g. 19.81, 36.74).
Additionally, I think that the Qur’an deliberately ignores naming the members of the Trinity. Verse 4.171 rejects the concept of “three” and verse 5.73 describes that concept as the belief that “Allah is one of three.” What is being rejected, therefore, is not the unity of a particular group of three, but the very concept of threesome — that God is three beings, aspects, modes, manifestations, or whatever. The Qur’an focuses on rejecting the concept of the unity of three rather than who those three are. As I have already said, the Qur’an considers the Trinity a form of tritheism, and no playing with words can make the Trinity a form of monotheism.
Verse 5.75 makes the interesting observation that both Jesus and his mother ate food, which is a sign of being human. Having to eat food in order to live is used elsewhere in the Qur’an as a sign that the messengers were ordinary human beings:
And We did not send before you [O Muhammad!] other than men to whom We gave revelation, so ask the people of the remembrance if you do not know. (21.7) And We did not make them bodies that do not eat food, and they were not immortal. (21.8)
And they (the disbelievers) say: “What is the matter with this Messenger (Muhammad) that he eats food and walks in the markets? Why has an angel not been sent down to him, so that he should have been a warner with him?” (25.7)
And We have not sent before you [O Muhammad!] any messengers but they ate food and walked in the markets. And We have made some of you a test for others: will you have patience? And your Lord is ever seeing. (25.20)
I should stress another important point. A common mistake in studying the Qur’an’s discussion of Christian beliefs, including the doctrine of the Trinity, is to suggest that the Qur’an talks about the New Testament only, or simply misunderstands it. The Qur’an rejects particular Christian beliefs, regardless of whether they are found in the New Testament or not. For instance, the Qur’an rejects the worship of Mary, even though Mariolatry is not a New Testament doctrine. The New Testament does not have any special scriptural value outside mainstream Christianity, which was itself defined in the first few centuries after Jesus. The Qur’an is interested in clarifying its positions on doctrines that Christians hold, regardless of the origin of those doctrines.