Well in general for any question, you can do the following:
The question is something like
"If A, then B".
So given that A is true, show that B is true, something like that. Well, what you are meant to do is work from the fact of A to tell you something about B. Then you integrate it with your other knowledge to give you the answer.
So what pokka did was he took the condition A, e.g. tan(x) = t and he used that information to work out the sides of a triangle where tan(x) = t. Then he looked at what he was asked to prove, and he used that information to prove it.
Similarly with 2), he took the condition tan(A) = k*tan(B) and turned it into a statement about sin(A), sin(B), cos(A) and cos(B). There's a good hint to do this because the statement you're trying to prove is in terms of those 4 ratios. Then, he took the LHS of what you were asked to prove, used the condition plus his knowledge, and showed it was equal to the RHS.
