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Would you say the word 'reciprocate' (in the context of responding to a courtesy/greeting question by returning the exact same question) is too formal a word to expect in casual conversations.
When someone greets you with 'how are you?', you have to ask back.
Many thanks in advance.
Respond in kind.
In kind (Oxford): In the same way; with something similar.
Examples (also from Oxford):
‘Treat the players right, and they will respond in kind.’
‘The least that can be done is to take him seriously and to respond in kind.’
‘In kind, I ask him to withdraw and apologise because I do not like his claiming that I am a stooge of anyone else.’
‘I was finding it difficult to respond in kind to his teasing.’
‘And he responded to me in kind last night saying that he understood that and that it was an attack against him.’
Your example:
When someone greets you with 'How are you?', you should respond in kind.
Reciprocate is perfect, even in informal conversation. I would reserve more rare words, such as requite, for writing, because half the population will need to refer to a dictionary. By the way, many Americans do not answer the greeting "How are you?" at all. They simply repeat the question. In many instances, "How do you do?" would be repeated, also. It irks me a bit, but that's life. My students in China were quite formal. If I greeted one with "Hello. How are you today?" they would reply "Fine, thank you. How are you?" Americans often will reply "I'm well," which makes me wonder if they have been ill.
Ask back does not work very well, because it does not carry the specific meaning of ask[ing] back the same question.
You might try reflect back, but I would not use the word must, because you are not compelled to answer back by asking the same question, you could offer a response about how you actually are.
So for instance in your example you might say:
When someone greets you with 'how are you?', you might reflect the question back to them.
I think the most idiomatic way of saying it would be
"in turn"
John asked Mary a question and she asked, in turn, "why should I answer that?"
in turn Oxford Living Dictionary PHRASE
1In succession; one after the other.
‘everyone took it in turn to attack my work’
1.1 Used to convey that an action, process, or situation is the result of a previous one.
‘he would shout until she, in her turn, lost her temper’
I have also heard "asked in return" ... but I do not think that is as idiomatic.
Requite is the first word that comes to mind, and while it could work it doesn't mean exactly the same as reciprocate. Requite refers more to return the favor or something similar to that.
Asking someone to reflect back would probably have them think that have to ponder the question, that there's something more to it, something for them to think about.
Tit for tat (tip for tap), either will work for this, would also kind of work. Though this is usually used for an act of retaliation.
