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

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 -  \(\frac{1}{x^2}\))