IS Repentance merely turning from unbelief to belief?

If repentance has nothing to do with sin and is merely turning from unbelief to belief as many today teach, then surely these demons were saved.

Matthew 8:29  And, behold, they cried out, saying, What have we to do with thee, Jesus, thou Son of God? art thou come hither to torment us before the time?
30  And there was a good way off from them an herd of many swine feeding.
31  So the devils besought him, saying, If thou cast us out, suffer us to go away into the herd of swine.
32  And he said unto them, Go. And when they were come out, they went into the herd of swine: and, behold, the whole herd of swine ran violently down a steep place into the sea, and perished in the waters.
 
These demons clearly believed in Jesus, recognizing him as the Son of God, and even acknowledging his authority over them.

The Bible tells us that they all believe and even tremble at the knowledge of God, but that is not repentance.

James 2:19  Thou believest that there is one God; thou doest well: the devils also believe, and tremble.

According to the apostle Paul, our repentance is toward God while faith is toward Christ. We turn from our disobedience and rebellion toward a holy God and put our faith in Jesus Christ, the only one who can save us from our sin.
Turning from sin to God is repentance. Turning to Christ in belief is faith.

Repentance is essential for belief; because it is sin that hardens us against belief.
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Hebrews 3:13  But exhort one another daily, while it is called To day; lest any of you be hardened through the deceitfulness of sin.