Yes, Muslims need to believe in all four books i.e, Torah, Zaboor, Injeel (a.k.a Bible) and the Holy Qur'an. However, Muslims have to follow just one of them i.e., The Holy Qur'an. Because Qur'an is the final book for the final Prophet sent for the entire humanity for there to come until the judgement day. Moreover, all other books except the Qur'an have been altered with by humans; Qur'an could and can never be altered with because its protection's responsibility is taken by Allah Almighty himself. So, the Muslims have to believe in all books but follow just one.
As an example of alteration in Bible.The Old Testament contains 613 rules. The New Testament contains 1,050 rules. Some of the rules contain:
How can such cruel and inhumane orders be given to humans by God himself. They have been altered with and Qur'an describes that. So, now to follow the right path, you have to follow Qur'an.
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