The correct answer to the question is option 1, Alexander Cunningham. Alexander Cunningham was a British archaeologist who played a significant role in the identification and exploration of ancient sites in India. He is often referred to as the "father of Indian archaeology."

Cunningham conducted extensive research and study of ancient Indian texts, including Buddhist scriptures, which mentioned the city of Taxila. He compared the descriptions and references in these texts with the geographical and topographical features of the region to determine the probable location of Taxila.

His diligent efforts led him to identify the ancient city of Taxila, also known as Takshshila, in present-day Pakistan. Taxila was a major center of learning and a prominent city in ancient India, known for its universities and intellectual pursuits.

It is important to note that while Cunningham made the initial identification of Taxila, subsequent excavations and research by other archaeologists, such as R.D. Banerji, John Marshall, and Daya Ram Sahni, further contributed to the understanding and exploration of the ancient city. However, in terms of the specific identification of Taxila mentioned in the question, Alexander Cunningham is credited with the initial discovery.