$\text{ If }\mathrm{\theta }\text{ is the angle between the lines }\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1$ $\text{ and }\frac{\mathrm{x}}{\mathrm{b}}+\frac{\mathrm{y}}{\mathrm{a}}=1\text{. Find the value of }\sin \mathrm{\theta }\text{ when }\mathrm{a}>\mathrm{b}$

$$\begin{gathered} \text{ Given lines are} \\ \frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1\Rightarrow \mathrm{bx}+\mathrm{ay}-\mathrm{ab}=0 ...\left(1\right) \end{gathered}$$
$and \frac{\mathrm{x}}{\mathrm{b}}+\frac{\mathrm{y}}{\mathrm{a}}=1\Rightarrow \mathrm{ax}+\mathrm{by}-\mathrm{ab}=0 ...\left(2\right)$
$\begin{array}{l}Now \sin \mathrm{\theta }=\frac{\left|{\mathrm{a}}_1{\mathrm{b}}_2-{\mathrm{a}}_2{\mathrm{b}}_1\right|}{\sqrt{{\mathrm{a}}_1^2+{\mathrm{b}}_1^2}\sqrt{{\mathrm{a}}_2^2+{\mathrm{b}}_2^2}}\\ =\frac{\left|{\mathrm{b}}^2-{\mathrm{a}}^2\right|}{\sqrt{{\mathrm{b}}^2+{\mathrm{a}}^2}\sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2}}\\ \\ \Rightarrow \sin \mathrm{\theta }=\left|\frac{{\mathrm{b}}^2-{\mathrm{a}}^2}{{\mathrm{b}}^2+{\mathrm{a}}^2}\right|\end{array}$