If cosecθ = √5 and θ is acute, the value of (2 − si$n^2$θ)/(1 + co$t^2$θ) is:

sinθ = 1/√5 so si$n^2$θ = 1/5, and the denominator 1 + co$t^2$θ is just cose$c^2$θ = 5. The value is $(2-1/5)/5=(9/5)/5=9/25=0.36$. Forgetting to divide by the denominator leaves 9/5.