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

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</mfrac> </mrow> </mfrac> </msqrt> <mtext> </mtext> </mrow> <mrow> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mi> x </mi> </mfrac> <mo> - </mo> <mi> y </mi> </mrow> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mfrac> <mi> y </mi> <mi> x </mi> </mfrac> <mo> + </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </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> <mo> + </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msqrt> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mi> x </mi> </mfrac> <mo> - </mo> <mi> y 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<msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mi> x </mi> </mfrac> <mo> - </mo> <mi> y </mi> </mrow> </mfrac> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> x </mi> </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> <mo> + </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> 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2007-05-02