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

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</mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> <mi> &#960; </mi> </mfrac> </mrow> <mo> &#8971; </mo> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> 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