This study investigates if the drug tadalafil can help Veterans with Chronic Obstructive Pulmonary Disease (COPD) and high blood pressure in the lungs, known as Pulmonary Hypertension (PH), breathe easier. Tadalafil is a medication that helps widen blood vessels and improve blood flow. In this study, 126 Veterans will be randomly assigned to receive either tadalafil or a placebo (an inactive pill that looks like tadalafil) without knowing which one they're taking. The study will last for 6 months with check-ins at 1, 2, 3, 4, 5, and 6 months by clinic visits or phone calls. During these check-ins, researchers will monitor side effects and the Veterans' safety. They will also assess changes in shortness of breath, quality of life, and lung function.

• The study lasts for 6 months and requires multiple check-ins.
• Participants will be randomly given tadalafil or a placebo without knowing which.
• Researchers will monitor safety and side effects throughout the study.