without hesitation / reassured
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without hesitation
Expresses that one can do something without worries, concerns, or hesitation; confidently.
Du kannst mir getrost die Wahrheit sagen, ich werde nicht böse sein.
You can tell me the truth without hesitation; I won't be angry.
'Getrost' (without hesitation/reassured) is closely related to the noun 'der Trost' (comfort) and the verb 'trösten' (to comfort). It describes a state in which one has been comforted and is therefore without worry.
Nach dem Gespräch fühlte sie sich getröstet.
After the conversation, she felt comforted.
In its modern meaning, 'getrost' (without hesitation) is almost always used as an adverb that modifies a verb. It then means 'ohne Bedenken' (without concern) or 'ruhig' (go ahead / calmly). Use as an adjective before a noun, e.g. 'ein getroster Mensch', is uncommon.
Du kannst das Auto getrost hier parken, es ist sicher.
You can park the car here without hesitation; it's safe.
The meaning 'getröstet sein' (to be comforted) is outdated and sounds poetic or elevated today. It is found mainly in older literature or in the fixed encouragement 'Sei getrost!' (Be reassured!).
Sei getrost, wir werden eine Lösung finden.
Be reassured; we will find a solution.
quiet / calm
'ruhig' and 'getrost' can both mean that you can do something without worry or concern. In this use, 'ruhig' is very conversational and sounds natural in sentences like 'Du kannst ruhig fragen' (Feel free to ask). 'getrost' has almost the same meaning, but sounds a little more elevated or more definite. Both fit when you want to reassure or encourage someone. In normal conversation, 'ruhig' is often the simpler choice; 'getrost' sounds a little more deliberately phrased.
Wegen der guten Ergebnisse könnt ihr die Übung getrost überspringen.
Because of the good results, you can skip the exercise without hesitation.
Ihr könnt ruhig schon anfangen, ich komme gleich nach.
You can go ahead and start already; I'll join you in a moment.