What is the meaning of 疑ってどうすんですか?

Question:

i know that 疑る means to doubt, どう means how, and 住む　means to live. But I can't get the meaning out of them.

Answer:

it is 疑って　どう　する　の　ですか？
どう　する　の　became どうすん　in shortened form.

疑って　means to doubt.
どう　means how / what.
する to do
の　is complement
ですか　makes the sentence question form.
It litreally means , "What would you do by douting it?"
Actual meaning is "It seems we have no choice but to trust it." , "Let's trust it.", "You are the person to trust it.", "It's better to trust it." .... ...