The phrases “trust in Christ” or “trust in Jesus” are often used in Christian circles as formulas for salvation. They are, of course, derived from the fact that Scripture says that salvation is “by grace through faith” (Eph. 2:8-9), and Scripture also contains frequent references to believing in Christ. A few times, the KJV uses the word “trust” where most modern translations use “believe.” In any case, “trust in Christ” and “believe in Christ” are both biblical phrases.
If you ask, however, some who often use the phrase “trust in Christ” regarding what they mean, they will often explain that people are either trusting in their “works” to get them into heaven, or they are “trusting Christ.” Thus, “trusting Christ” is actually equivalent to nothing more than trusting Christ to get you to heaven rather than trusting in your works.