Impossible proof of Pythagoras theorem
In the 1968 book entitled "The Pythagorean Proposition" by Elisha Scott Loomis, which has documented 371 distinct proofs of Pythagoras theorem, it is claimed that there is no possible proof using trigonometry since all identities of trigonometry are proved using Pythagoras theorem and hence a trigonometric proof results in a circular logic. However this is not the case. In 2009 Jason Zimba has proved [1] Pythagoras theorem using trigonometry avoiding circular logic. His simple proof involves defining sine and cosine angles using similar right angled triangles and then presenting a geometric proof of sine and cosine of the subtraction angle formula and finally leading to the Pythagoras theorem. Reference: [1] Zimba, J., 2009. On the possibility of trigonometric proofs of the Pythagorean theorem. In Forum geometricorum (Vol. 9, pp. 1-4). Link: https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf