If it's said without a potato in the speaker's mouth, it's Norwegian. With a potato, it's Danish.
Asking the real questions
If you see the sentence written, it's hard to know, but if you hear it, oh boy, I guarantee you will be immediately able to tell the difference :-)
Denne sætning er dansk.
Denne setning er norsk.
Den første er dansk og den anden er norsk og dette er begge.
Jokes about incomprehension aside, it does depend if it's Nynorsk or Bokmål.
Se on suomea!
Is norjalainen and tanskalainen correct?
Theoretically yes, in practice no. Those words are adjectives referring to nationality or origins. Using them here sounds likes asking which country's passport the sentences have. :)
What about norjaksi and tanskaksi?
Most of the time I can't even tell with the exception of a few give away words and or differences in spelling
In a previous, similar example tai was used and the explanation was that it's one or the other and not a choice that includes both or neither.
Agreed, tai should be allowed because there are definitely sentences that could be both.
Both are accepted. :)