Final answer:
Austria became independent in 1804, joined Hungary in a dual monarchy as the Austro-Hungarian Empire, and became an independent nation again after WWI in 1918. It was annexed by Nazi Germany in 1938 during the Anschluss and was occupied by the Allies until regaining independence in 1955.
Step-by-step explanation:
The Country That Became Independent in 1804 and Joined as a Dual Monarchy with Hungary
The country that became independent in 1804 is Austria, which was tightly associated with the Habsburgs and established the Austrian Empire during that year. Following a period of significant nationalistic movements and political restructuring in Europe, Austria, along with Hungary, formed the Austro-Hungarian Empire in 1867 as a dual monarchy.
This complex political structure collapsed at the end of World War I in 1918, at which time Austria became an independent nation once again. However, this independence was short-lived because in 1938, Austria was annexed by Nazi Germany during the Anschluss. After World War II, Austria was occupied by Allied forces until 1955, when it regained its independence and eventually joined the European Union in 1995.
Discontent simmered in the Austro-Hungarian Empire as different ethnic groups sought autonomy, with the Hungarians achieving near-complete independence in the dual monarchy arrangement. Yet, this arrangement led to a spread of nationalist problems rather than their resolution.
Austria's exclusion from German affairs post-1866 conflict with Prussia further complicated its political landscape, compelling it to forge an alliance with Hungary despite separate national governments and parliaments.