It could be said that mathematics is the language of physics. That is another way of better understanding what is physics. Numerical values, units of measurement, and similar concepts are all mathematical in nature, and are used to describe physical quantities in the most accurate and precise manner.
In brief: Cough headache. There are a couple of possibilities. Coughing can raise the pressure inside your head, which can cause pain sometimes. There is also a poorly-understood entity called the primary cough headache,  that is associated with coughing, straining, laughing, crying, etc.
Usually coughing never become the reason for back pain, but if someone is suffering from cough from long time then their cough went into the blood. So while coughing it put pressure on their blood vessels which turns to contraction of blood vessels or we can say blood vessels are getting pulled while coughing. Because of ever end ever coughing it put pressure in back and results get pain in back.