항등식의 확인

1. FullSimplify[ArcTan[x] - ArcSin[Sqrt[x^2/(1 + x^2)]]] Table[% /. {x -> Random[], y -> Random[]}, {20}] // Chop

1. f[x_, n_] := Hypergeometric2F1[(1 - n)/2, (1 + n)/2, (x + 1)/2, 1/2] g[x_, n_] := (Sqrt[Pi] 2^((1 - x)/2) Gamma[(x + 1)/2])/( Gamma[1/4 (x - n + 2)] Gamma[1/4 (x + n + 2)]) Table[{f[x, n], g[x, n]} /. {n -> RandomReal[{-10, 10}], x -> RandomReal[{0.1, 10}]}, {20}] // TableForm