We know that cos²θ + sin²θ = 1, so cos²θ = (1 - sin²θ) = (1 - sinθ)(1 + sinθ), and
cos²θ/(1 - sinθ) = (1 - sinθ)(1 + sinθ)/(1 - sinθ) = (1 + sinθ) with restriction sinθ ≠ 1, or θ ≠ π(n+1/2), n=1,2,3,... .