Final answer:
Great Britain recognized Brazil's independence primarily due to economic interests in trade with the country. The relationship established by opening Brazilian ports to British trade after the relocation of the Portuguese monarchy to Brazil set the stage for this recognition.
Step-by-step explanation:
Great Britain was one of the first countries to recognize Brazil's independence due to economic interests in Brazilian trade. The answer to the question is b. Economic interests in Brazilian trade. History shows that after the relocation of the Portuguese monarchy to Brazil, Brazilian ports were opened to all friendly nations, which essentially favored Great Britain. All previous manufacturing prohibitions intended to protect Portuguese industry were revoked, strongly benefiting British economic interests.
During that period, Brazil had a significant transition when the Portuguese royal family and court moved to Rio de Janeiro. This move resulted in Brazil's elevation to a kingdom on equal footing with Portugal, centralizing control in Rio, which became a strong unifying factor for the nation. After its independence, Brazil, unlike other Latin American countries that formed republics, was governed by a monarch, which showcases another aspect of the continuity with its colonial legacy.