믿다 - to believe, to trust (in something, someone) 믿을 수 없어요 = "I can't believe it" 보다 - [in this context] to try. --> i find sometimes 보다 doesn't always translate into English as a strong meaning of 'try'. For instance, to try something is a stronger indication of an attempt than 'give it a shot' 'we will see', which is softer. 믿어 보자 = 1. Let's try to believe (in something, someone) 2. Let's believe (in something, someone) I'm not a native speaker, this is what i think. Hope it helps.

To add a bit, it's very similar in nuance to "give (something) the benefit of the doubt". So "믿어 보자" is like "Let's give it the benefit of the doubt".

I think "let's try to believe , let's believe" is a correct meaning. To help you understand, here's a dialogue using "믿어보자" that I made ^^ =================================================================== 엄마 : 아빠가 새해 결심(new year's resolution)으로 담배를 끊으시겠대. 딸 : 글쎄, 작년에도 똑같은 결심하시지 않으셨어요? 이번에는 지키실 수 있을까요? 엄마 : 그래도 이번에는 지키시지 않을까? 한번 믿어보자.