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If cosec θ + cot θ = 3 ; what is the value of cosecθ.cotθ ? |
1 \(\frac{3}{4}\) \(\frac{20}{9}\) \(\frac{22}{9}\) |
\(\frac{20}{9}\) |
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 - \(\frac{1}{9}\)) = \(\frac{80}{36}\) = \(\frac{20}{9}\) |
