$If {(\sin a + \cos eca)}^2+{(\cos a + seca)}^2 = k + {\tan }^2 a + co{t}^{2}a , then k =$

$$\begin{gathered} {(\mathrm{sin\theta }+\mathrm{cosec\theta })}^2+{(\mathrm{cos\theta }+\mathrm{sec\theta })}^2=\mathrm{k}+{\tan }^2\mathrm{\theta }+{\cot }^2\mathrm{\theta } \\ {\sin }^2\mathrm{\theta }+{\mathrm{cosec}}^2\mathrm{\theta }+2+{\cos }^2\mathrm{\theta }+{\sec }^2\mathrm{\theta }+2=\mathrm{k}+{\tan }^2\mathrm{\theta }+{\cot }^2\mathrm{\theta } \\ 5+1+{\cot }^2\mathrm{\theta }+1+{\tan }^2\mathrm{\theta }=\mathrm{k}+{\tan }^2\mathrm{\theta }+{\cot }^2\mathrm{\theta } \\ \mathrm{k}=7 \end{gathered}$$