>Supposing we want to prove a theorem (or any other problem)
>in Geometry or Tringonometry (any branch of Maths), what
>steps should we take. Ofcourse we must see the given data
>and what we have to prove but are there any other factors?
>

I would recommend the books by G.Polya, especially How to Solve It? and that of J. Mason, Thinking Mathematically. Check

http://www.math.utah.edu/~alfeld/math/polya.html