Final answer:
The correct form of the possessive adjective in this sentence is 'mon'.
Step-by-step explanation:
The correct form of the possessive adjective in this sentence is mon. The sentence should be: Je suis mon cousin(e).
The possessive adjective 'mon' is used to indicate possession of a masculine singular noun. In this case, 'cousin(e)' is singular and can refer to either a male or female cousin.
Other forms of possessive adjectives in French are: ma (feminine singular), mes (plural), ton (informal), ta (informal feminine singular), tes (informal plural), son (masculine or feminine singular).
Learn more about Possessive adjectives in French