Not sure what i'm getting wrong. Here is the question.

I used the Pythagorean theorem, therefore arc(x) = opp/adj, hence my hypotenuse was x+1 since (x^2+1)^1/2, Now I assume that Sec^2= Hyp^2/Adj ^2. The result just seems wrong and it doesn't help me prove arctan, thx fox the help.