If cosec θ + cot θ = 3 ; what is the value of cosecθ.cotθ ?
Answer & explanation
Correct answer: option 3
cosec θ + cot θ = 3
⇒ cosec θ - cot θ = \(\frac{1}{3}\)
4cosecθ.cotθ = (cosecθ + cotθ)2 - (cosecθ - cotθ)2
⇒ 4cosecθ.cotθ = 32 - \(\frac{1}{3^2}\)
⇒ cosecθ.cotθ = \(\frac{1}{4}\)(9 - \(\frac{1}{9}\)) = \(\frac{80}{36}\) = \(\frac{20}{9}\)