There are other texts, that distinguish between each.
Body and Soul:
Mic 6:7 Will the LORD be pleased with thousands of rams, or with ten thousands of rivers of oil? shall I give my firstborn for my transgression, the fruit of my body for the sin of my soul?
Matt. 10:28 And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.
Soul and Spirit:
1 Sam. 1:15 And Hannah answered and said, No, my lord, I am a woman of a sorrowful spirit: I have drunk neither wine nor strong drink, but have poured out my soul before the LORD.
Job 7:11 Therefore I will not refrain my mouth; I will speak in the anguish of my spirit; I will complain in the bitterness of my soul.
Heb. 4:12 For the word of God is quick, and powerful, and sharper than any twoedged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart.
Spirit and Body:
Daniel 7:5 I Daniel was grieved in my spirit in the midst of my body, and the visions of my head troubled me.
1Cor. 6:20 For ye are bought with a price: therefore glorify God in your body, and in your spirit, which are God’s.
James 2:26 For as the body without the spirit is dead, so faith without works is dead also.
BTW, trichotomy is not an exclusive WOF teaching, many Baptists , Pentecostals and other Evangelicals teach this.