The coordinate transformation x = tan(1/2 ∂) cos ∅, y = tan(1/2 ∂) sin ∅ can be used to show that the spherical line element 

equals the planar line element dx2 +dy2 multiplied by a position-dependent function f(x,y). Determine f(x,y).

ds? = do? + sin? vdg? = f(x, y) (da? + dy?) %3D