If cosθ/(1 − sinθ) + cosθ/(1 + sinθ) = 4 and θ is acute, then θ equals:

Over the common denominator 1 − si$n^2$θ = co$s^2$θ the numerator is cosθ(1 + sinθ) + cosθ(1 − sinθ) = 2cosθ, so the left side collapses to 2cosθ/co$s^2$θ = 2secθ. Then 2secθ = 4 gives secθ = 2, cosθ = 1/2 and θ = 60°. Reading the left side as 2cosθ would demand cosθ = 2, which is impossible; taking cosθ = 1/2 to mean 30° confuses the ratio with its co-ratio, and 45° would make the left side 2√2 ≈ 2.83.