If a = x sec $\theta$+ y tan$\theta$ , b = x tan$\theta$ +ysec$\theta$ then $x^2–y^2 =$

$\begin{array}{lcl} & & \begin{array}{rcl}\mathrm{a}& =& \mathrm{x} \mathrm{sec\theta }+\mathrm{y} \mathrm{tan\theta }\end{array}\\ & & \begin{array}{rcl}\mathrm{b}& =& \mathrm{x} \mathrm{tan\theta }+\mathrm{y} \mathrm{sec\theta }\end{array}\\ & & \begin{array}{rcl}{\mathrm{a}}^2-{\mathrm{b}}^2& =& {\mathrm{x}}^2 {\sec }^2\mathrm{\theta }+{\mathrm{y}}^2 {\tan }^2\mathrm{\theta }+2\mathrm{xysec\theta } \mathrm{tan\theta }-{\mathrm{x}}^2{\tan }^2\mathrm{\theta }-{\mathrm{y}}^2{\sec }^2\mathrm{\theta }-2\mathrm{xy} \mathrm{sec\theta } \mathrm{tan\theta }\end{array}\\ & =& \left({\mathrm{x}}^2-{\mathrm{y}}^2\right) {\sec }^2\mathrm{\theta }-\left({\mathrm{x}}^2-{\mathrm{y}}^2\right) {\tan }^2\mathrm{\theta }\\ & =& \left({\mathrm{x}}^2-{\mathrm{y}}^2\right) \left({\sec }^2\mathrm{\theta }-{\tan }^2\mathrm{\theta }\right)\\ & =& {\mathrm{x}}^2-{\mathrm{y}}^2\\ & & \begin{array}{lcl}{\mathrm{x}}^2-{\mathrm{y}}^2& =& {\mathrm{a}}^2-{\mathrm{b}}^2\end{array}\\ & & \\ & & \end{array}$