The value of $\frac{sec θ \,  cosec θ}{2+tan^2θ+cot^2θ}$ is equal to :

sec θ cosec θ sec θ sin θ sin θ cos θ cos θ cosec θ

sin θ cos θ

\(\frac{sec θ.cosec θ}{2 + tan²θ+cot² θ }\) = \(\frac{sec θ.cosec θ}{1 + tan²θ +1 +cot² θ }\) { sec²θ - tan²θ = 1   & cosec²θ - cot²θ = 1 } = \(\frac{sec θ.cosec θ}{ sec²θ . cosec² θ }\) = \(\frac{1}{ secθ . cosec θ }\) = cosθ . sin θ