Preheat oven to 375 degrees F (190 degrees C). Lightly grease baking sheets.
Cream butter or margarine, shortening, white sugar and confectioners' sugar together until light and fluffy. Beat in the egg and the vanilla.
Sift the flour, baking soda, salt and cream of tartar together. Add the flour mixture to the sugar mixture and blend.
Shape dough into walnut-sized balls and place on the prepared baking sheets. Dip a glass in white sugar and press balls flat. Bake at 375 degrees F (190 degrees C) for 10 to 12 minutes or until lightly browned.