1tsp glycerine is part of the cake mix (gluten free recipe) so not sure whether it could be subbed?
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It's such a small amount I think you can just leave it out. Typically glycerin is used in icing to thin it out, like in fondant that can be difficult to work with. It adds a bit of sweetness and retains a little moisture. If 1/2 tsp is all your recipe calls for I would just skip it. While I haven't seen your entire recipe, I have been baking gluten free for years without a need for glycerin. Good luck!
I think Potato is probably right, but do make sure you've got something in the recipe (xanthan gum, guar gum, tapioca starch, potato starch, corn starch, etc.) that's going to help it bind together. Some GF recipes will use glycerine in this function and unless you've got something else doing the job, your recipe might fail if you leave it out. If you've got one of the things I listed in the recipe, you're probably fine just ignoring it. If not, add 1tsp xanthan or guar gum, or 2-3 Tbls tapioca or potato starch just to be on the safe side.
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