Simplify sin θ/(1 + cos θ) + (1 + cos θ)/sin θ.

Common denominator: [si$n^2$θ + $(1+cos\theta {)}^2$]/[sin θ(1 + cos θ)] = (2 + 2cos θ)/[sin θ(1 + cos θ)] = 2/sin θ = 2 cosec θ.