Why is that there is no tangent law?

Question

We know that, in a triangle ABC, sine law and cosine law are well developed formulas.

My questions are:-

1. Why is that there is no tangent law? (If no, just hope that someone can devise one someday.)

2. Can the identities like $\tan A + \tan B + \tan C = \tan A\tan B\tan C$ be qualified?

2'. If it does not qualify, is it because it (1) is too difficult to use; or (2) has no practical value wrt applications; or (3) has no sides involved.

Answer 1

There is a law called as tangent law. $$\color{red}{\text{But the thing is all these results are equivalent.}}$$ If you want you can deduced cosine rule from sin rule.
Also if you want you can deduced sine rule from cosine rule.
As I think using one of theses rules and the relation $A+B+C=\pi$ we can solve any triangle.