36) The Koran explicitly claims divine inspiration, but the New Testament books do not. How do you know that the New Testament books are nevertheless inspired, but the Koran is not?

The same way the early church didn't accept books which claimed to be inspired, and authored by apostles, God authenticates His Word to His children.

It is because God is good and upright that He delights in teaching sinners the right way, and to accomplish that He must identify His word to them.

Ps 25:8-9
8 Good and upright is the LORD: therefore will he teach sinners in the way.
9 The meek will he guide in judgment: and the meek will he teach his way.

Ps 25:12
12 What man is he that feareth the LORD? him shall he teach in the way that he shall choose.

Isa 54:13
13 And all thy children shall be taught of the LORD; and great shall be the peace of thy children.

Jer 31:33-34
33 But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
34 And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.


John 6:45
45 It is written in the prophets, And they shall be all taught of God. Every man therefore that hath heard, and hath learned of the Father, cometh unto me.

John 16:13-14
13 Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.
14 He shall glorify me: for he shall receive of mine, and shall shew it unto you.

1 Cor 2:10-12
10 But God hath revealed them unto us by his Spirit: for the Spirit searcheth all things, yea, the deep things of God.
11 For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God.
12 Now we have received, not the spirit of the world, but the spirit which is of God; that we might know the things that are freely given to us of God.

Eph 1:17
17 That the God of our Lord Jesus Christ, the Father of glory, may give unto you the spirit of wisdom and revelation in the knowledge of him:

In context, John is saying the Holy Spirit's anointing grants the Elect perception into all things (that were then happening in their congregation), where the spirit of antichrist inspired a false gospel, and that they could "know, perceive" what was "of God" and what wasn't....John also gives an objective test of the spirit behind a message....whether they listen to the apostles or not 1 John 4:6 (= sola scriptura):

I Jn 2:20-21
20 But ye have an unction from the Holy One, and ye know all things.
21 I have not written unto you because ye know not the truth, but because ye know it, and that no lie is of the truth.


I Jn 2:27
27 But the anointing which ye have received of him abideth in you, and ye need not that any man teach you: but as the same anointing teacheth you of all things, and is truth, and is no lie, and even as it hath taught you, ye shall abide in him.


John 10:27 My sheep hear my voice, and I know them, and they follow me:

Hebrews 4:12 For the word of God is quick, and powerful, and sharper than any twoedged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart.

Isaiah 8:20 To the law and to the testimony: if they speak not according to this word, it is because there is no light in them.

__________________
The times of this ignorance God winked at; but now commandeth all men every where to repent:

Behold, I stand at the door, and knock: if any man hear my voice, and open the door, I will come in to him, and will sup with him, and he with me.-kjv