If I have broken headphones can i trade them in for a new pair at the apple store?

If your Apple headphones are defective, they are covered by the standard one-year warranty of the iPhone (or optional extended coverage). If purchased separately, the standard warranty is one year from purchase date. If it's "broken" due to accidental damage (or beyond coverage period), it's not covered by warranty. If you have AppleCare+ on the iPhone, there may be additional benefits

https://www.apple.com/support/products/iphone.html

If your situation is unclear, you should contact Apple's official customer support

Contact - Official Apple Support

Apple does not take broken headphones for trade ins.