$\frac{1}{x y \sin (x y)}$ and Taylor two variables ,Two Points representation

Question

I have been reading about the title and I found the following Series $$\frac{7 (x-1)^2 (x+1)^2 y^2}{360 x^2}+\frac{7 y^2}{360 x^2}+\frac{1}{x^2 y^2}+(x-1) (x+1) \left(\frac{7 y^2}{180 x^2}-\frac{367}{360 x^2}+\frac{\csc (1)}{x^2}\right)-\frac{367}{360 x^2}+\frac{\csc (1)}{x^2}$$ without demostration Wolfram Alpha calculate the Taylor series abou x=1 and y=-1 the grade two( for simplify) $$(x-1) \left((y-1) \left(2 \csc (1)+2 \cot ^2(1) \csc (1)+\cot (1) \csc (1)\right)+(y-1)^2 \left(-\frac{3 \csc (1)}{2}-3 \cot ^3(1) \csc (1)-\cot ^2(1) \csc (1)-\frac{7}{2} \cot (1) \csc (1)\right)-\csc (1)-\cot (1) \csc (1)\right)+(x-1)^2 \left((y-1)^2 \left(\frac{11 \csc (1)}{4}+6 \cot ^4(1) \csc (1)+8 \cot ^2(1) \csc (1)+\cot (1) \csc (1)\right)+(y-1) \left(-\frac{3 \csc (1)}{2}-3 \cot ^3(1) \csc (1)-\cot ^2(1) \csc (1)-\frac{7}{2} \cot (1) \csc (1)\right)+\frac{3 \csc (1)}{2}+\cot ^2(1) \csc (1)+\cot (1) \csc (1)\right)+(y-1)^2 \left(\frac{3 \csc (1)}{2}+\cot ^2(1) \csc (1)+\cot (1) \csc (1)\right)+(y-1) (-\csc (1)-\cot (1) \csc (1))+\csc (1)$$ I try to representation to see the difference and the result was the first ii much better as simple view , the first series it is come from?