Recall [tex] \csc^2\theta=\cot^2\theta+1[/tex]
or, $\csc^2\theta-\cot^2\theta=1 \implies (\csc\theta+\cot\theta)(\csc\theta-\cot\theta)=1$
Now, $\cot \theta - \csc \theta = P$
$\implies (-P)(\csc\theta+\cot\theta)=1$
or $(\csc\theta+\cot\theta)=-\frac{1}{P}$
