How does faith relate to righteousness in a Christian's life?
Answered in 2 sources
Faith is the means by which Christians lay hold of the righteousness of Christ, not a work that contributes to it.
In the life of a Christian, faith is a divine gift that allows believers to trust in the righteousness of Christ. It is not seen as a work that earns righteousness, but rather as the means through which they lay hold of the perfect righteousness that Jesus provides. Ephesians 2:8-9 makes it clear that salvation is by grace through faith, not of works, so that no one can boast. Thus, the faith of a believer is a response to God's revelation of righteousness through Christ, affirming that they are justified and accepted by grace alone.
Commentary