The Pharisees and the Sadducees actually disliked and disagreed with each other. They were only united by two things, first, by their hatred for the gospel of Christ, and second, by their love for power.
They were forced to unite to control the Sanhedrin, but they were not of one mind.
Acts 23:6a NKJV
“But when Paul perceived that the one part were Sadducees, and the other Pharisees, he cried out in the council,”
Paul made two claims that divided the Sanhedrin. Firstly, he claimed to be a Pharisee, and secondly, he claimed to be defending the doctrine of the resurrection of the dead.
Acts 23:6 NKJV
“…he cried out in the council, Men and brethren, I am a Pharisee, the son of a Pharisee: of the hope and resurrection of the dead I am called in question.”
The Pharisees on the council supported Paul, because he said he was one of them, and also because he claimed to believe one of their doctrines.
“Then there arose a loud outcry. And the scribes of the Pharisees’ party arose and protested, saying, “We find no evil in this man; but if a spirit or an angel has spoken to him, let us not fight against God.”
The Sadducees were against Paul because he claimed to be a member of the opposing party and also because he believed in the resurrection.
Acts 23:8 NKJV
“For Sadducees say that there is no resurrection—and no angel or spirit; but the Pharisees confess both.”
Paul was trying to divide the Sanhedrin and he succeeded totally.
Acts 23:10 NIV
“The dispute became so violent that the commander was afraid Paul would be torn to pieces by them. He ordered the troops to go down and take him away from them by force and bring him into the barracks.”
The Lord Jesus had the final say.
Acts 23:11 NKJV
“But the following night the Lord stood by him and said, “Be of good cheer, Paul; for as you have testified for Me in Jerusalem, so you must also bear witness at Rome.”
May you be of good cheer. May you fulfill the plans of Jehovah for your life. May your enemies be scattered, in Jesus’ name.