If $\mathrm{x}=Se\mathrm{c\theta }=\mathrm{tan\theta }; \mathrm{y}=\mathrm{cosec\theta }+\mathrm{cot\theta }$ then $\mathrm{xy}+1=$

$$\begin{gathered} x=sec\theta -\tan \theta , y=\cos ec\theta +cot\theta \\ xy=sec\theta \cos ec\theta -\tan \theta \cos ec\theta +sec\theta cot\theta -\tan \theta cot\theta \\ xy=\frac{{\sin }^2\theta +{\cos }^2\theta }{\sin \theta \cos \theta }-sec\theta +\cos ec\theta -1 \\ xy+1=\tan \theta +cot\theta -sec\theta +\cos ec\theta \\ xy+1=\cos ec\theta +cot\theta -(sec\theta -\tan \theta ) \\ xy+1=y-x \end{gathered}$$