Let us assume that a tangential impact is made on the planet by another cosmic body in a plane passing through its axis

Let us assume that a tangential impact is made on the planet by another cosmic body in a plane passing through its axis of rotation. Will this lead to a change in the inclination of the planet’s axis of rotation to the orbital plane?

Not. This will cause the rotation axis to precess. The inclination of the axis of rotation to the orbital plane will remain the same.

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