What is the evidence of Holy Trinity?

The Holy Trinity in the Bible

God the Father sent his angel Gabriel to promise Mary God the son through the Holy Spirit

Luke 1:35 And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God.

Detailed Reference:

John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God. 14 The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth. 

John 1:10 He was in the world, and the world was made by him, and the world knew him not.

John 1:17 For the law was given through Moses; grace and truth came through Jesus Christ. 18 No one has ever seen God, but the one and only Son, who is himself God and[b] is in closest relationship with the Father, has made him known.

John 1:29 The next day John saw Jesus coming toward him and said, “Look, the Lamb of God, who takes away the sin of the world! 

John 1:33 And I myself did not know him, but the one who sent me to baptize with water told me, ‘The man on whom you see the Spirit come down and remain is the one who will baptize with the Holy Spirit.’ 34 I have seen and I testify that this is God’s Chosen One.”

The Holy Trinity that is mentioned in the Quran

Surah 4:171 confirms that Jesus, was born of the spirit, the word of God, and he is Lord of heaven and earth and about his Father in heaven, agreement with the words of the Bible.

يَا أَهْلَ الْكِتَابِ لَا تَغْلُوا فِي دِينِكُمْ وَلَا تَقُولُوا عَلَى اللَّهِ إِلَّا الْحَقَّ ۚ إِنَّمَا الْمَسِيحُ عِيسَى ابْنُ مَرْيَمَ رَسُولُ اللَّهِ وَكَلِمَتُهُ أَلْقَاهَا إِلَىٰ مَرْيَمَ وَرُوحٌ مِنْهُ ۖ فَآمِنُوا بِاللَّهِ وَرُسُلِهِ ۖ وَلَا تَقُولُوا ثَلَاثَةٌ ۚ انْتَهُوا خَيْرًا لَكُمْ ۚ إِنَّمَا اللَّهُ إِلَٰهٌ وَاحِدٌ ۖ سُبْحَانَهُ أَنْ يَكُونَ لَهُ وَلَدٌ ۘ لَهُ مَا فِي السَّمَاوَاتِ وَمَا فِي الْأَرْضِ ۗ وَكَفَىٰ بِاللَّهِ وَكِيلًا

O People given the Book(s)! Do not exaggerate in your religion nor say anything concerning Allah, but the truth; the Messiah, Eisa the son of Maryam, is purely a Noble Messenger of Allah, and His Word; which He sent towards Maryam, and a Spirit from Him; so believe in Allah and His Noble Messengers; and do not say "Three"; desist, for your own good; undoubtedly Allah is the only One God; Purity is to Him from begetting a child; to Him only belongs all whatever is in the heavens and all whatever is in the earth; and Allah is a Sufficient Trustee (of affairs).

Other references to the Holy Trinity in the Bible

Hebrews 9:14. How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?

John 14:16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever; 17Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.

1 Corinthians 6:19 What? know ye not that your body is the temple of the Holy Ghost which is in you, which ye have of God, and ye are not your own? 20For ye are bought with a price: therefore glorify God in your body, and in your spirit, which are God's.

Matthew 28:19-20: “Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything that I have commanded you. And surely I am with you always, to the very end of the age.”

Other mentions of the plurality of Godhead in the Qu'ran

Surah 78:6  God refers to himself as “Our” Spirit,  the Bible confirms the same God+Son+Spirit called Trinity

وَمَرۡيَمَ ٱبۡنَتَ عِمۡرَٰنَ ٱلَّتِيٓ أَحۡصَنَتۡ فَرۡجَهَا فَنَفَخۡنَا فِيهِ مِن رُّوحِنَا وَصَدَّقَتۡ بِكَلِمَٰتِ رَبِّهَا وَكُتُبِهِۦ وَكَانَتۡ مِنَ ٱلۡقَٰنِتِينَ

(66:12) Allah has also set forth the parable of Mary, the daughter of Imran,²⁶ who guarded her chastity,²⁷ and into whom We breathed of Our Spirit,²⁸ and who testified to the words of her Lord and His Books. She was among the obedient. 26.

God refers to himself as “We” Surah 78:6 

وَالْجِبَالَ أَوْتَادًا وَخَلَقْنَاكُمْ أَزْوَاجًا وَجَعَلْنَا نَوْمَكُمْ سُبَاتًا وَجَعَلْنَا اللَّيْلَ لِبَاسًا وَجَعَلْنَا النَّهَارَ مَعَاشًا وَبَنَيْنَا فَوْقَكُمْ سَبْعًا شِدَادًا وَجَعَلْنَا سِرَاجًا وَهَّاجًا وَأَنْزَلْنَا مِنَ الْمُعْصِرَاتِ مَاءً ثَجَّاجًا لِنُخْرِجَ بِهِ حَبًّا وَنَبَاتًا وَجَنَّاتٍ أَلْفَافًا

6. “Have We not made the earth as a (wide) expanse?” 7. “And the mountains as pegs?” 8. “And We created you in pairs,” 9. “And We made your sleep for repose,” 10. “And We made the night as a covering” 11. “And We made the day for (seeking) livelihood,” 12. “And We built above you seven firmaments” 13. “And We made (therein) a blazing lamp,” 14. “And We sent town from the clouds water in abundance” 15. “That We may bring forth thereby grain and plants,” 16. “And gardens of luxurious growth?”

The appearance of God as three persons in Torah:

אוַיֵּרָא אֵלָיו יְהוָה בְּאֵלֹנֵי מַמְרֵא וְהוּא יֹשֵׁב פֶּתַח הָאֹהֶל כְּחֹם הַיּוֹם. בוַיִּשָּׂא עֵינָיו וַיַּרְא וְהִנֵּה שְׁלֹשָׁה אֲנָשִׁים נִצָּבִים עָלָיו וַיַּרְא וַיָּרָץלִקְרָאתָם מִפֶּתַח הָאֹהֶל וַיִּשְׁתַּחוּ אָרְצָה.גוַיֹּאמַר אֲדֹנָי אִם נָא מָצָאתִי חֵן בְּעֵינֶיךָ אַל נָא תַעֲבֹר מֵעַל עַבְדֶּךָ. דיֻקַּח נָא מְעַט מַיִםוְרַחֲצוּ רַגְלֵיכֶם וְהִשָּׁעֲנוּ תַּחַת הָעֵץ. הוְאֶקְחָה פַת לֶחֶם וְסַעֲדוּ לִבְּכֶם אַחַר תַּעֲבֹרוּ … 1.

The Lord appeared to him [Abraham] by the oak trees of Mamre [Hebron]; he [Abraham] was sitting at the entrance of the tent as the day grew hot. 2. Looking up, he [Abraham] saw three men standing near him. As soon as he saw them, he ran from the entrance of the tent to greet them and, bowing to the ground, 3. he said, “Adonai , if it please you, do not go on past your servant. 4. Let a little water be brought; bathe your feet and recline under the tree. 5. And let me fetch you a morsel of bread that you may refresh yourselves; then go on…”