You are really one of the rare animals.
In fact, all you have to do is tell the truth. It's best to take some pictures of the library with your mobile phone to show your parents, so that they can know that you are really studying instead of going out to play, so that they will believe you.
I have to say, your parents don't trust you enough, but this lack of trust is probably based on your past record can't support their trust. In other words, you may not like studying at ordinary times and often go out to play, or you always find some excuses to deceive them and make them think that you are doing business, but you are actually going out to play. I suggest you do this less in the future and do everything when you go out.
You think you can make up a perfect lie to make your parents believe you completely, but you should know that your parents have experienced what you are like now, your parents have thought about what you are thinking now, and they may have done what you have done, so they can say that they know everything about your mind and what you are doing.
In this case, telling the truth and getting scolded is better than telling a lie to cheat them into trusting for a while and finally being discovered by their parents. Although you were not scolded, your parents no longer trust you.
So, please don't lie to them under any circumstances. Otherwise, you will end up like this. Obviously, he did something good, but no one believed him.