Explanation

Write p = (1 − sinθ)/cosθ and q = (1 + cosθ)/sinθ. Expanding p + q(p − 1) and using sin²θ + cos²θ = 1, the expression simplifies identically to −1 for every admissible θ (e.g. at θ = 45°, p ≈ 0.4142 and q ≈ 2.4142 give 0.4142 + 2.4142·(−0.5858) = −1). Hence option A.