Can I use a chess book to check the first 2-3 moves of an opening in Daily Chess?

Can I use a chess book to check the first 2-3 moves of an opening in Daily Chess or it is against the Fair Play rules? Or maybe I just have to learn the variation lines by heart?

Не знаю...

Наверное можешь

I think you can, but I am not sure. You can also ask chess.com support team about this I guess.

Daily/correspondence has different rules to live games. For Daily/correspondence you ARE allowed opening books as long as it doesn't include engine evaluations (no computer stuff), but even opening databases and game databases are allowed! 

Conversely, in live games (online or in-person) books and databases (engine evaluations or not) are NOT allowed. 

In short, yeah your chess book should be okay (for daily, but not live games) as long as it doesn't have engine evaluations.

Thank you!

Daily Chess (days per move)

--The below are NOT ALLOWED--

• Engines - You may not use any engines to analyse ongoing games! This includes Chessmaster, Fritz, Komodo, Lc0, Stockfish, Chessbase with any active UCI engine, etc. 
• Tablebases - Tablebases are chess databases that contain every possible move for endgames of up to 7 pieces. These sequences will always lead to a win when a win is possible, and are for that reason the same as asking an engine to analyse a position. Tablebases are not allowed! 
• Help from other people - You are not allowed to ask for help from another person! Do not ask anyone for advice on any of your ongoing games! Do not let anyone else play on your account!
• Fixing game results - Arranging games, playing with multiple accounts or losing intentionally are also against the rules!

--The below are ALLOWED--

• Books - You may consult chess books, lessons, or videos to search for a good move. These resources do not involve an engine that finds an answer for you, so are okay for Daily games!
• Opening databases - You may look at opening databases, or game records to find a good move. You may NOT use any of these that also use an engine to evaluate the best moves! 
• The in-game self-analysis tool - You may use the self analysis tool to look at possible moves and to set conditional moves. This is only available in Daily games! 

See https://support.chess.com/article/317-what-counts-as-cheating-on-chess-com for more information.

You can use . I never play daily chess

Does that mean when my opponent plays Traxler countergambit, I can use chess book to play 20 moves theory?

yes

The following rules apply to ANY GAME CURRENTLY IN PROGRESS:
• For “Live” games (as in ‘over-the-board’ i.e. OTB, games) it is ILLEGAL to consult or employ ANY external aid or resource, including human assistance.
• For “Daily” games (as in so-called ‘correspondence’ chess) it is LEGAL to consult passive resources such as books, articles, online databases, opening explorers, etc. However, it is ILLEGAL to use computers/chess engines to calculate moves, or to consult with another human about the game,

Можно, но только в заочных и только дебютные справочники. Использовать аналитический модуль для поиска хода нельзя.