None
but for this case especial:
that are Half angle formulas and I show you the born of this formulas, the Half angle formulas born too for this
now for Sum or Difference as a Product, is only an identity
to tangent is easily deducible but if you want that i post the formulas, only ask for it
forgive me, i'm a bit tired, but i don't see how what you did helps us to derive the law of cosines.
@Gregorio556: there is no sense in someone re-inventing the wheel. the proof to the cosine rule is something one can easily find by doing a google search or using some other search engine. you may even find several ways of dong it. good luck. you can come back here if you have trouble with one of the derivations and we can work through it