Let A be the relation defined on the set of all real numbers such that $\mathrm{A}=\left\{(\mathrm{x},\mathrm{y}):{\sec }^2\mathrm{x}-{\tan }^2\mathrm{y}=1\right\}$ then A is:

$$\begin{gathered} (\mathrm{x},\mathrm{y})\in \mathrm{A}\therefore {\sec }^2\mathrm{x}-{\tan }^2\mathrm{x}=1,\left(\mathrm{x}\ne \frac{(2\mathrm{n}+1)\mathrm{\pi }}{2}\right) \\ (\mathrm{x},\mathrm{y})\in \mathrm{A}\Rightarrow {\sec }^2\mathrm{x}-{\tan }^2\mathrm{y}=1\Rightarrow \left({\tan }^2\mathrm{x}+1\right)-\left({\sec }^{2}y-1\right)=1 \\ \begin{array}{l}\Rightarrow {\sec }^2\mathrm{y}-{\tan }^2\mathrm{x}=1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em} \Rightarrow (\mathrm{y},\mathrm{x})\in \mathrm{A}\\ (\mathrm{x},\mathrm{y})\in \mathrm{A}\text{ and }(\mathrm{y},\mathrm{z})\in \mathrm{A}\hspace{0.25em} \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\Rightarrow (\mathrm{x},\mathrm{z})\in \mathrm{A}\end{array} \end{gathered}$$
A is symmetric, transitive but not reflexive.