Ps4 – try before I buy on Playstation

As long as your console's language is set to Danish and the game supports Danish localization, the game will be in Danish.

If your console is set to a language that is not included in your game, the game will run in the first language listed in the game's metadata, which appears to be sorted alphabetically according to their English abbreviation (i.e. GER for "German" instead of DE for "Deutsch").
More specifically: if your console is set to English and you try to launch a game that has been localized only in German, French and Italian, the game will run in French forcing others to set their console's language to German or Italian unless they can live with French localization.

Only very few games allow you to set the language instead of relying on the console's language and falling back to some weird default in case of failure; Metal Gear Solid 5: Ground Zeroes is one such game, although it is a bit of a special case. You can specify the language for everything text based, such as subtitles and menus, but not for voice-overs. The game is either voiced in Japanese for the Japanese version, or in English for the International version.

In short: Yes, if the version you bought features Danish localization, you can play the game in Danish, but only if your console's system language is set to Danish as well or the game allows you to set the language manually.

To be on the safe side, you should use the PS4 Recovery Mode to re-install the system software via USB (Option 3). You should only download the official firmware update from https://www.playstation.com rather than rely on third-party or unofficial sources.

If you want to be extra safe, you should do a full backup of the console to a external hard drive and then reset the PS4 using Option 7 from the PS4 Recovery Mode. This will delete everything on the console, including the system software, saved data and games, so use with caution. Once reset, you can either restore your backed-up data or download your games again.