Why should we believe in whats written in Vedas?

Lord Sri Krishna says: “I am situated in everyone’s heart, and from Me come remembrance, knowledge, and forgetfulness. By all the Vedas am I to be known; indeed I am the compiler of Vedanta, and I am the knower of the Vedas”. [Bhagavad-gita 15.15] Thus the words of the Vedas are the supreme authority.

One may ask, “How may one accept authority?” The answer is given by Srila Prabhupada: “The answer of the genuine mother to the question of who is one’s father is authoritative”. One cannot argue about or object to this point. Similarly, when a child learns that two times two is equal to four from his father and he tells the same thing to a professor of mathematics, the professor has to agree that the child is speaking perfectly. The child may not be perfect, but the knowledge that he is speaking is perfect because he has taken it from an authority. Similarly, all the Vedic knowledge is infallible. For example, it has been mentioned in the Vedas that cow dung is pure whereas another stool is impure, and modern science has found this to be true. It has been scientifically confirmed by chemical analysis that cow dung indeed contains various antiseptic properties.

Source: A.C. Bhaktivedanta Swami Prabhupada (2012 edition), “The Scientific Basis of Krishna Consciousness”, Page 44