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In my textbook, the addition of alkaline $\ce{KMnO4}$ to fumaric acid (trans) is stated as a syn-addition even though $\ce{OH}$ is present on opposite sides in the product.
But,the defination of syn-addition is:
Addition of electrophile and nucleophile on the available sites on the same side of molecule.
Isn’t this contradictory?
I don’t know what molecule you ended up with, but the way I draw it, I end up with (2S,3S)-2,3-dihydroxysuccinic acid as shown below.
The syn-addition step would technically be the addition of the electrophile permanganate to the double bond. From there, the oxygens are in place and are not moved. If you reorder the structure to the identical zig-zag representation, you should arrive at a clear syn-orientation.
Note that there are two rotations in this: the first step includes a rotation of fumaric acid by $90^\circ$ so that I can draw the five-membered ring in a plain. After cleaving off $\ce{MnO4^3-}$ (which further reacts to $\ce{MnO4^2-}$ in basic conditions) I arrive at the syn-product.
With maleic acid, everything would be the same, except for the orientation of the carboxylic groups in the second and third structures. That would lead to the hydroxyl groups pointing in different directions even though we are still dealing with a syn-addition.
