If cosecθ + cotθ = P find the value of (P^2-1)/(P^2+1)

Let us assume a triangle.

Put in → cosecθ + cotθ = P

\(\frac{Hyp.}{Perp}\)+\(\frac{Base}{Perp.}\)=P

\(\frac{5}{3}\)+\(\frac{4}{3}\)=P

P = 3

Now, \(\frac{P^2-1}{P^2+1}\)=\(\frac{9-1}{9+1}\)=\(\frac{8}{10}\) =\(\frac{4}{5}\) =\(\frac{B}{H}\)= cosθ