The value of (sec θ cosec θ)/(2+tan^2θ+cot^2θ) is equal to :

\(\frac{sec θ.cosec θ}{2 + tan²θ+cot² θ }\)

= \(\frac{sec θ.cosec θ}{1 + tan²θ +1 +cot² θ }\)

{ sec²θ - tan²θ = 1   & cosec²θ - cot²θ = 1 }

= \(\frac{sec θ.cosec θ}{ sec²θ . cosec² θ }\)

= \(\frac{1}{ secθ . cosec θ }\)

= cosθ . sin θ