Complex sentence: Perhaps the simplest example of a nontrivial tangent bundle is that of the unit sphere "S" 2: that this tangent bundle is nontrivial is a consequence of the hairy ball theorem.
Split into simpler sentences: Perhaps the simplest example of a nontrivial tangent bundle is that of the unit sphere "S" 2. That the tangent bundle of "S" 2 is nontrivial is a consequence of the hairy ball theorem.