What three "lands' did the Muslims secure in the east?

Byzantine, Persian, and Indian lands came under the control of Muslims.

Through the use of conquest, the Muslim empire was able to expand eastward conquering the Byzantine and Persian Empires as well as the Indian peninsula. The famed Byzantine capital of Constantinople was transformed to a new capital of Istanbul. Muslim leaders allowed for religious practices to continue in the conquered areas and even maintained some of the laws and government practices, but the influence of the Islamic Empire were found in law, culture, and religion in all of these places.

The Islamic Prophetic Muhammad recognized a new integrated organization in the Arabian Headland and conquered the lands in the east part; these lands are the Sassanid Empire and Monophysites in Syria, Byzantine Egypt, and Palestine which caused in the association of an influential Muslim state all over the peninsula.