## **Core Concept**
The patient's presentation of hoarseness, hemoptysis, and a hard painless lump in the left supraclavicular fossa is highly suggestive of a malignant process, particularly lung cancer with metastasis to the supraclavicular lymph node (Virchow's node). The symptoms and signs point towards a advanced stage of cancer.

## **Why the Correct Answer is Right**
The correct approach in this scenario involves confirming the diagnosis through tissue pathology. Given the patient's symptoms and the presence of a palpable supraclavicular lymph node, the most appropriate diagnostic step would be to perform a **biopsy** of the lymph node. This procedure will provide a definitive diagnosis by allowing histopathological examination of the tissue. The presence of cancer cells in the lymph node confirms metastatic disease, and the type of cancer cell can guide further management.

## **Why Each Wrong Option is Incorrect**
- **Option A:** While imaging studies (like CT scans) are crucial in staging the disease and assessing the extent of tumor spread, they do not provide a tissue diagnosis.
- **Option B:** A sputum cytology might be helpful in diagnosing lung cancer if the tumor is centrally located and shedding cells into the airways, but it's less likely to be diagnostic in this case where the primary symptoms suggest a more advanced stage with lymph node involvement.
- **Option C:** Although a chest X-ray can provide initial clues to lung pathology, it does not offer a tissue diagnosis and is not sufficient for planning treatment in a case with suspected metastatic cancer.

## **Clinical Pearl / High-Yield Fact**
A key clinical pearl is that a painless, hard lymph node in the supraclavicular fossa, especially in a smoker, is highly suggestive of malignancy until proven otherwise. The presence of such a node necessitates prompt investigation, with biopsy being a critical step for diagnosis.

## **Correct Answer:** . Biopsy of the supraclavicular lymph node.