Dependent samples are paired measurements for one set of items while independent samples are measurements made on two different sets of items
If the values in one sample reveal no information about those of the other sample, then the samples are independent. However, if the values in one sample reveal information about those of the other sample, then the samples are dependent.
From the above descriptions, we see that the effectiveness of a headache medicine is measured by the intensity of headaches in patients before and after drug treatment.
Thus, It is a dependent sample because it is a paired measurement of the intensity of headache before and after drug treatment for a set of item (which is the effectiveness of the headache medicine). Also, it is a dependent sample because the value in one sample (before drug treatment) reveals information about the other sample (after drug treatment).
Therefore, it is a dependent sample.