**Core Concept**
Acute hirsutism and hoarseness of voice in a young female patient can be indicative of an androgen-secreting tumor, particularly a virilizing tumor such as an adrenal or ovarian tumor. This condition can disrupt the normal balance of sex hormones, leading to excessive androgen levels.

**Why the Correct Answer is Right**
The best investigation for diagnosing an androgen-secreting tumor would be a **Selective Renein Assay (SRA)**. This test measures the levels of renin in the blood, which can help differentiate between primary and secondary hyperaldosteronism. In cases of an androgen-secreting tumor, such as an adrenal tumor, the renin levels are typically suppressed. A low renin level can indicate an adrenal tumor, whereas a high renin level would suggest a renal cause.

**Why Each Wrong Option is Incorrect**
**Option A:** **Cortisol levels** - While cortisol levels may be elevated in Cushing's syndrome, which can also present with hirsutism and virilization, it is not the most specific test for an androgen-secreting tumor.

**Option B:** **Thyroid function tests** - Thyroid function tests are not directly related to the diagnosis of an androgen-secreting tumor.

**Option C:** **LH and FSH levels** - Measuring LH and FSH levels can help assess the pituitary-gonadal axis, but it is not the best investigation for diagnosing an androgen-secreting tumor.

**Clinical Pearl / High-Yield Fact**
A key aspect to remember is that a low renin level in the presence of hypertension and virilization can be suggestive of an adrenal tumor. This is a classic exam trap, and it is essential to remember the interplay between the renin-angiotensin-aldosterone system and the hormonal axis in diagnosing endocrine disorders.

**Correct Answer:** D.