If x = sec θ - tan θ and y = cosec θ + cot θ, then which one of the following is correct?

x = sec θ - tan θ = (1 - sin θ)/cos θ, y = cosec θ + cot θ = (1 + cos θ)/sin θ. Note: xy = (1 - sin θ)(1 + cos θ)/(sin θ cos θ). Testing θ = π/4: x = √2 - 1, y = √2 + 1, xy = 1. Then x - y + xy + 1 = (√2-1) - (√2+1) + 1 + 1 = 0. So option (b) is correct.