A 39 year old woman with hypertension and hypokalaemia is most likely to have which condition?

The condition associated with hypertension and hypokalaemia in this case is Conn's syndrome, also known as primary hyperaldosteronism. This syndrome is caused by an excess production of aldosterone from the adrenal glands, which leads to sodium retention, increased blood volume, hypertension, and increased potassium excretion, resulting in hypokalaemia.

The presence of both hypertension and hypokalaemia is particularly indicative of Conn's syndrome. Patients may present with resistant hypertension, and additional features can also include muscle weakness, fatigue, and other symptoms of electrolyte imbalance due to low potassium levels.

Cushing's syndrome, while it can also cause hypertension, typically presents with a wide array of other symptoms including abnormal glucose metabolism, central obesity, and facial changes, but not specifically hypokalaemia. Hyperparathyroidism primarily affects calcium metabolism and does not usually cause hypertension or hypokalaemia. Phaeochromocytoma mainly presents with episodic hypertension, palpitations, sweating, and anxiety but is not typically associated with hypokalaemia.

In summary, the combination of hypertension and hypokalaemia aligns most closely with Conn's syndrome due to its mechanistic effects on aldosterone levels and resultant electrolyte imbalance.