The Portuguese came to India with the aim of establishing a monopoly over the spice trade. At the time the spice trade was dominated by the Ottoman Turks and the Arabs. Spice was an important commodity as it acted as a natural preservative for foods in the harsh European winters.
While they could trade with the Ottomans and Arabs, the price of this trading was too exorbitant for the European economy. As such the Portuguese and other Europeans sought a direct trade route to India that would bypass the Turks and Arabs. This is the reason why the Portuguese came to India.
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