Godly repentance and faith work together. In some ways, they are two sides of the same coin. Each will lead to the other. And like two sides of the same coin, you can't have one without the other.
Godly repentance means turning away from our former, carnal way of life and towards obedience to God and living according to God's law. It means repenting of our sinful nature and our sins, what the Bible calls "dead works" (Hebrews 6:1-2).
Sin is the transgression of God's law (1 John 3:4), so repenting of sin means setting our hearts and minds to obey God's law.
But God's law requires faith because faith is one of the three weightier matters of the law (Matthew 23:23). Faith is believing what God says. So when we repent, we agree and commit ourselves to believe God, to have faith in His word.
Believing what God says is also required by the spiritual intent of the first great commandment, to love God with all our being, because it is God's will and desire that we believe and trust Him, and if we really love God with all our being, we will give God our trust and belief in His word.
Anyone who says, "I will stop sinning, but I don't trust God and I won't believe what He says," has not fully repented. God wants faith and trust in Him to be a motivation for us to obey. Repentance requires faith.
Godly repentance then includes and leads to faith in God and His word, a willingness and commitment to trust and believe everything He tells us. Faith is part of the way of life we commit to at baptism.
But also, godly faith leads to repentance.
If we trust God and believe what He says, we will agree with God that His way of life is best and that we should repent and turn from our sins and live according to His spiritual law.
Faith is more than believing that God exists. Satan and his demons know that God exists. "You believe that there is one God. You do well. Even the demons believe—and tremble!" (James 2:19). But do they believe in God's way of life? Do they believe God's way of life, living according to His commands and laws, is the best way of life, the way they should live? Do they believe the teachings of Jesus Christ, that it is better to give than to receive (Acts 20:35)? I don't think so, or else they would live that way of life.
The first sin recorded in the Bible may be Lucifer's sin of vanity. "Your heart was lifted up because of your beauty; You corrupted your wisdom for the sake of your splendor" (Ezekiel 28:17). From this, all other sins seem to have come as a result.
But Lucifer was a free moral agent, and if he was the first being to sin, that means no one tempted him. God must have taught Lucifer and all the angels the right way of life and he must have warned them of the consequences of vanity and sin so they could avoid it.
Once Lucifer allowed vanity to enter his mind, his thinking became more and more twisted and perverted and evil. By exalting himself in a spirit of vanity, he corrupted his own mind - "You corrupted your wisdom for the sake of your splendor". He became more evil as sin led to more corruption of mind and the corruption of his mind lead to more sin. And because sin brings suffering, Lucifer, now Satan, God's enemy, has brought misery and suffering upon himself and others. And he can never go back because he can never think clearly enough to choose to go back.
Yet God, in love, must have warned Lucifer of the consequences of living the way of life of vanity and self-exaltation instead of God's way of outgoing concern and love for others. The Bible shows with example after example that it is God's way to warn. Yet Lucifer, even after being warned of consequences, made the choice that destroyed his chance for eternal happiness.
Why would Lucifer do this? He could not have wanted to be miserable.
He was not tempted as we are tempted. We feel tempted to sin because Satan tempts us. But when Lucifer first sinned, there was no other evil being to tempt him. And God did not tempt him or create any evil nature in Lucifer that Lucifer would have to resist or struggle against (James 1:13).
Yet Lucifer, without any evil influence in the universe to pull and tempt him to do wrong, sinned. Why?
The only reason I can think of is that he didn't believe God's warnings. He didn't trust God that God was telling him the truth, that vanity and self-seeking would ruin him. He probably never experienced mental suffering before he sinned. He had no experience with sin or the consequences of sin. For him to truly know and understand what consequences would be in store for him if he sinned, he would have to believe God and take God's word for something he never experienced for himself. He would have to trust God, that God knew what He was talking about and was telling the truth. And apparently Lucifer was not willing to do that.
So he chose to exalt himself. He experimented with vanity. He trusted his own thinking and his own experimenting and chose to learn by experience which way of life is best. Maybe he thought his own self-centered, vain, competitive way of life would lead to a greater level of happiness than he already had. Or maybe he wasn't sure but wanted to learn from experience, to do an experiment, to find out for himself what sin and the consequences of sin would be like. If that was the case, he took a chance, a gamble, and lost. God was telling him the truth, but Lucifer didn't believe Him. Lucifer may have been the originator of "gambling". He threw the dice, so to speak, betting that God was lying or mistaken, and he lost. He may also be the originator of the "scientific method" of rejecting divine revelation and only accepting knowledge that comes from experimentation, observation, and interpretation of results.
Lucifer lacked faith when he chose to sin.
God does not want another Satan in His Kingdom. Once was enough.
God is building in His children the character of faith so He will know that we will always believe His word, for eternity, without doubting, without second guessing, without thinking we have to experiment to see if God is telling the truth.
We have to learn the lesson of faith, the lesson of believing and trusting God's word unconditionally, before He will let us into His kingdom.
For a related post, see "Day of Atonement" in this blog, published September 16, 2010, link:
Here are links to related chapters or sections in Preaching the Gospel:
CHAPTER 6 - OBTAINING GOD'S HELP -- PRACTICING WHAT WE PREACH