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

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

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

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

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