If $\mathrm{m}=\mathrm{Sin\theta }+\mathrm{Cos\theta }; \mathrm{n}=\mathrm{Sec\theta }+\mathrm{Cosec\theta }$ then

$\begin{array}{rcl}\mathrm{m}& =& \mathrm{sin\theta }+\mathrm{cos\theta }\\ {\mathrm{m}}^2& =& 1+2\mathrm{sin\theta } \mathrm{cos\theta }\\ \mathrm{sin\theta } \mathrm{cos\theta }& =& \frac{{\mathrm{m}}^2-1}{2}\\ \mathrm{n}& =& \mathrm{sec\theta }+\mathrm{cosec\theta }\\ {\mathrm{n}}^2& =& {\sec }^2\mathrm{\theta }+{\mathrm{cosec}}^2\mathrm{\theta }+2\mathrm{sec\theta } \mathrm{cosec\theta }\\ {\mathrm{n}}^2& =& \frac{1}{{\sin }^2\mathrm{\theta } {\cos }^2\mathrm{\theta }}+\frac{2}{\mathrm{sin\theta } \mathrm{cos\theta }}\\ {\mathrm{n}}^2& =& \frac{{\mathrm{m}}^2}{{\left({\displaystyle \frac{{\mathrm{m}}^2-1}{2}}\right)}^2}\\ \mathrm{n}& =& \frac{2\mathrm{m}}{{\mathrm{m}}^2-1}\\ \mathrm{n}\left({\mathrm{m}}^2-1\right)& =& 2\mathrm{m}\end{array}$