In the early 9th century AD______ produced accurate sine and cosine tables and the first table of tangents.
A. Habash al-Hasib al-Marwazi.
B. Muhammad ibn Jabir al-Harrani al-Battani
C. Muhammad ibn Musa al-Khwarizmi.
D. Abu al-Wafa al-Bujzani.

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Hint: Muhammad ibn Musa al-Khwarizmi, a pioneer in spherical trigonometry, was famous for his mathematical works that introduced Hindu-Arabic and algebra to European mathematics. The term ‘algorithm’ and algebra is believed to come from his name and the title of one of his works’ Elementary Algebra.’

Complete step by step answer:
In the early 9th century AD, Muhammad ibn Musa al-Khwarizmi produced accurate sine and cosign tables and the first table of tangents. Khwarizmi was one of the learned men who worked in the house of Wisdom in Baghdad. In ancient times, the study of trigonometry was flourishing in the Gupta period, especially due to Aryabhata who is known for discovering Sine function. During the middle ages, the mathematician Khwarizmi and Abu-al-Wafa continued the study of trigonometry. The earliest table of Sine functions is found in Surya Siddhanta (4th-5th century A.D.). The development of trigonometry tables and tables helped in the field of survey, astronomy, navigation, and understanding algebraic equations.
So, the correct answer is Option C.

Note: Khwarizmi’s treatise on algebra presented the first systematic solutions of linear and quadratic equations by completing the square. Hence, he is known as the father of algebra. He assisted in the construction of a world map for al-Ma Mun. based on Hindu and Greek sources, he compiled a set of astronomical tables. For example, a table of sine. He revised Ptolemy’s geography. It provided innovation in algebra and trigonometry. Through Latin translation, his works were spread. In the advancement of mathematics in Europe, his works played an important role.