THE INVERSE FUNCTION AND ITS DERIVATIVE: DEMONSTRATION

df/dx = tan ?1

dg/dy = tan ?2

tan ?1 tan ?2 = sin ?1 sin ?2 /cos ?1 cos ?2 =

sin ?1 sin (?/2 - ?1)/cos ?1 cos (?/2 - ?1) =

sin ?1 sin ?1 /cos ?1 cos ?1 = 1; ? tan ?1 = 1/tan ?2

or df/dx = 1/dg/dx

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