Why do doctors ask you to take a deep breath?

so you can relax and breathe normal

When doctors say this they should have a stethoscope on your back or chest because they are listening to the air rush in and out of your lungs.  They are trained to know the difference between normal lung sound and abnormal sounds.  Any abnormal lung sounds mean you are sick and need treatment.

The doctor is trained to hear abnormal sounds of the heart and lungs.  He or she may hear a heart murmur or abnormal breathing sounds in the bronchi tubes or lungs.  A trained ear is the key.  

To listen to your lungs if it has mucus in them you will hear a resistance. Also, that can be a bad thing.. so they always check during a physical.

They are trained to listen to sounds on the back of the lungs. Rasping sounds or congestion on exhalation or inhalation helps find asthma or other breathing issues.

When I place my stethoscope on your back or sides and ask you to take a deep breath, I'm listening to your breath sounds.

If I do so when my stethoscope is on the front of your chest, I'm trying to listen to your heart sounds without the interference of the breath sounds.

When I ask patients to take a deep breath, I'm usually listening to the air moving into and out of their lungs.  If you're normal and in a quiet room, they probably sound about the same.  However, in some conditions, sound become evident only when there is a quicker, deeper breath (like wheezing in early COPD).  Also, taking a big breath helps make the sounds louder, which is very helpful if there is any noise in the room.

Deep breaths can also accentuate certain heart murmurs or extra heart sounds, which can help distinguish between physiologic and pathological murmurs (or a fixed or variable S2, for instance).