The square root term corresponds to the length of the side opposite angle x in a triangle where angle x is the included angle between side length 2 and side length 1. This follows from the cosine rule a^2=b^2+c^2-2bccosA, where b=2 and c=1, and A=x. So a^2=5-4cosx. Geometrically, this can be represented by the triangle ABC, with sides a, b and c and included angle A. The tangent of A is then represented as a perpendicular BD from B on to AC (side length b) or AC extended, and/or CE from C on to AB or AB extended. Although the two perpendiculars BD and CE may be of different length, they each form the opposite side in two different right-angled triangles, so that opposite/adjacent=tanx, that is, BD/AD=CE/AE=tanx. AC=2 and AB=1 or AB=2 and AC=1, so the geometry doesn't necessarily help to simplify the expression, but it may help to work towards a geometrical solution by presenting a picture.