If ${(\sin \alpha +\text{cosec}\alpha )}^2+{(\cos \alpha +\sec \alpha )}^2=k+{\tan }^2\alpha +{\cot }^2\alpha$, then $k=$

${(\sin \alpha +\text{cosec}\alpha )}^2+{(\cos \alpha +\sec \alpha )}^2=k+{\tan }^2\alpha +{\cot }^2\alpha$

${\sin }^2\alpha +{\text{cosec}}^2\alpha +2\sin \alpha \text{cosec}\alpha +{\cos }^2\alpha +{\sec }^2\alpha +2\cos \alpha \sec \alpha$

$=1+{\text{cosec}}^2\alpha +2+2+{\sec }^2\alpha =1+1+{\cot }^2\alpha +2+2+1+{\tan }^2\alpha$

$={\cot }^2\alpha +{\tan }^2\alpha +7$

On comparing with R.H.S, we get $k=7$