If cosec θ + cot θ = x; what is the value of cosecθ.cotθ ?

\(\frac{1}{4}\)(x2 -  \(\frac{1}{x^2}\)) 2 -1 1

\(\frac{1}{4}\)(x2 -  \(\frac{1}{x^2}\))

cosec θ + cot θ = x ⇒ cosec θ - cot θ = \(\frac{1}{x}\) 4cosecθ.cotθ = (cosecθ + cotθ)2 - (cosecθ - cotθ)2 ⇒ 4cosecθ.cotθ = x2 - \(\frac{1}{x^2}\) ⇒ cosecθ.cotθ = \(\frac{1}{4}\)(x2 -  \(\frac{1}{x^2}\))