Question

What are the formulas for trigonometry and pythagoras?

Answer 1

That's not a good question at all.  It's a lot like asking
"What are the statements for News and President Obama ?"

There are at least a hundred formulas that are useful in trigonometry.
One of the most useful is:

       In a right triangle, the square of the length of the hypotenuse
       is equal to the sum of the squares of the two short sides.

Pythagoras is the name of the ancient Greek mathematician who
discovered that formula.  The formula is so useful that it's known
by his name, in his honor.