Final answer:
The most likely diagnosis for the patient is Diabetes insipidus, characterized by the chronic underproduction of antidiuretic hormone (ADH). This leads to excessive urination and water loss, causing dehydration and electrolyte imbalances.
Step-by-step explanation:
The most likely diagnosis for the patient with headache, weakness, polyuria, hypertension, tetany, hypernatremia, hypokalemia, and metabolic alkalosis is Diabetes insipidus. Diabetes insipidus is a condition characterized by the chronic underproduction of antidiuretic hormone (ADH), also known as vasopressin. This hormone helps regulate water balance in the body. In diabetes insipidus, there is a deficiency of ADH, leading to excessive urination and water loss, resulting in dehydration and electrolyte imbalances.