Using 'trust to' sometimes means you expect and accept that the outcome is not fully in your control. I didn't study, so I'll have to trust to luck on the exam.
Pro Tip 2/3
Not Always Rational
'Trust to' may imply a decision based on instinct rather than concrete evidence. She decided to trust to intuition rather than data.
Pro Tip 3/3
Potential Risk
Using 'trust to' can sometimes reflect a risky or hopeful approach to a situation. We're trusting to the weather being good for the picnic.