**Core Concept**
Gynaecomastia is a clinical condition characterized by the enlargement of breast tissue in males, often due to an imbalance between estrogen and androgen levels. Estimating the levels of various hormones can help identify the underlying cause of gynaecomastia.

**Why the Correct Answer is Right**
The correct answer is not directly related to the diagnosis of gynaecomastia. The primary hormones involved in this condition are estrogens (such as estradiol) and androgens (such as testosterone). Estimation of hormones like cortisol, aldosterone, and thyroid hormones (T3 and T4) may not be directly useful in investigating gynaecomastia. However, these hormones can be involved in secondary causes of gynaecomastia, such as Cushing's syndrome (cortisol), primary adrenal insufficiency or hyperaldosteronism (aldosterone), and hypothyroidism (T3 and T4).

**Why Each Wrong Option is Incorrect**
* **Option A:** Not useful in this context. Cortisol can be involved in secondary causes of gynaecomastia, such as Cushing's syndrome.
* **Option B:** Not directly useful in this context. Aldosterone is not typically involved in gynaecomastia, but primary adrenal insufficiency or hyperaldosteronism can be secondary causes.
* **Option C:** Not directly useful in this context. Thyroid hormones (T3 and T4) can be involved in secondary causes of gynaecomastia, such as hypothyroidism.

**Clinical Pearl / High-Yield Fact**
When investigating a case of gynaecomastia, it's essential to consider the patient's overall clinical picture, including symptoms and medical history, to identify potential underlying causes.

**Correct Answer:** D.