If ${ cosec }\theta -cot\theta =p$, then $cosec\theta +cot\theta =$

$\csc{\theta}-\cot{\theta}=p$

$\Rightarrow \left(\csc{\theta}-\cot{\theta}\right)\left(\csc{\theta}+\cot{\theta}\right)=p\left(\csc{\theta}+\cot{\theta}\right)$

$\Rightarrow {\csc}^{2}{\theta}-{\cot}^{2}{\theta}=p\left(\csc{\theta}+\cot{\theta}\right)$

$\Rightarrow 1=p\left(\csc{\theta}+\cot{\theta}\right)$

$\therefore \csc{\theta}+\cot{\theta}=\dfrac{1}{p}$