Math 111: Derivation of Tr.nometric Iden.ies. Many of the tr.nometric iden.ies can be derived in succession from the iden.ies: sin - = - sin ,. 1 cos - .Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! : reon .The main tr.nometric iden.ies between tr.nometric functions are proved, using mainly the 1.10.1 Proof of sine iden.ies; 1.10.2 Proof of cosine iden.ies..Derivations of Useful Tr.nometric Iden.ies. Pythagorean Iden.y. This is a basic and very useful relationship which comes directly from the definition of the .