Why did Europeans discover a new sea route to India?

The discovery of the sea route to India is the description sometimes used in Europe and among the Portuguese for the first recorded trip made directly from Europe to India via the Atlantic Ocean. It was undertaken under the command of Portuguese explorer Vasco da Gama during the reign of King Manuel I in 1497 -1499.
Mainly to avoid paying the Muslims. They do not want to pay the muslims for their articles.
India has had ancient trade networks with Europe that goes earlier than the Greek and Roman civilizations [as a part of the Tin Trade. Europeans have been visiting India for thousands of years and Indians have been doing the opposite trip.
While many Indians know that Europeans came to India, they don't know that the opposite happened too. There is the interesting story of Zarmonachegas - a Sramana philosopher sent by the Pandyan Kingdom of Tamil Nadu - who immolated himself in Athens 2000 years ago to prove his conviction to his philosophy. His tomb is still there in Greece. He and other philosophers brought Indian ideas to the West. This was instrumental in the development of Christianity (Buddhist influences of christianity.
You can also see the route in the given image..

The Portuguese traveled around the tip of Africa in order to reach India and avoid Muslim traders and Venetian middlemen while still cashing in on the lucrative spice trade. Before 1500, most European traders who did business with Asia were willing to allow Venetian traders a cut of the business, as they were willing to do business with the Muslim traders of North Africa. If one was a European Christian and wanted to travel overland in order to gain spices, one could travel through Byzantium and not have to worry about dealing with the Muslim influence in the Middle East and North Africa.
After 1453, with the fall of Byzantium, this route largely closed as the Ottoman Empire fined any non-Muslim trader moving through the area. While the trip around the Cape of Good Hope was quite dangerous and time-consuming, the spices brought back from India made the survivors of the journey very rich. India became a place for the spices and goods of Asia to come together, and many cities such as Calcutta became world-famous for their trade goods.