ArcCot[x] - ArcCsc[y] == ((Sqrt[1 + 1/x^2] x y Sqrt[(x - Sqrt[1 - 1/y^2] y)^2/((1 + x^2) y^2)])/ (x - Sqrt[1 - 1/y^2] y)) ArcSin[(Sqrt[1 - 1/y^2] + 1/(x y))/ Sqrt[1 + 1/x^2]] - (Pi Sqrt[1 + 1/x^2] x y Sqrt[(x - Sqrt[1 - 1/y^2] y)^2/((1 + x^2) y^2)])/ (2 (x - Sqrt[1 - 1/y^2] y)) + Pi (1 - (Sqrt[1 + 1/x^2] x y Sqrt[(x - Sqrt[1 - 1/y^2] y)^2/ ((1 + x^2) y^2)])/(x - Sqrt[1 - 1/y^2] y)) Floor[(Arg[(I - 1/x)/Sqrt[1 + 1/x^2]] + Arg[Sqrt[1 - 1/y^2] - I/y])/ (2 Pi)] - Pi (-1 - (Sqrt[1 + 1/x^2] x y Sqrt[(x - Sqrt[1 - 1/y^2] y)^2/ ((1 + x^2) y^2)])/(x - Sqrt[1 - 1/y^2] y)) Floor[-((-Pi + Arg[(I - 1/x)/Sqrt[1 + 1/x^2]] + Arg[Sqrt[1 - 1/y^2] - I/y])/(2 Pi))]

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<msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <mi> y </mi> </mrow> <mrow> <mi> x </mi> <mo> - </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> + </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mfrac> </mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> 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2007-05-02