What? You can! Are you sure you're installing the correct app? Make sure you're downloading it from the correct source[1]. I just doublechecked just right now just to confirm, and yes, you can trade using the Binance app. Because it would be pretty much useless to start with having a Binance app if you can't trade using it.

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[1] https://www.binance.com/clientDownloads.html