I don't know why the writer use 'to' before verb 'trust'. Following is the pattern used in a verb 'trust'
"trust somebody to do something"
Now, why we use 'to' before trust?
The managers did not know whom to trust.
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"To" makes the verb an "infinitive".
Here's an oversimplification: In most cases, a sentence can only have one real verb. (It's an oversimplification because I'm ignoring quotations, dependent clauses, and other such complex exceptions, but it works for these kinds of simple sentences).
In your sentence, "know" is the real verb, and "to trust" is actually the object. The object cannot be a simple verb, so it must be an infinitive instead. Basically, the infinitive "to" form of a verb allows one verb to act on another verb.
The easiest example of using an infinitive like this would be to construct sentences using "want".
I want to run. I want to sing. I want to jump.
One verb per simple sentence... the second "verb" is not grammatically treated as a verb. The infinitive makes it able to be an object.