Explanation

p+q = sin²θ and pq = −cos²θ, so p²+q² = (p+q)² − 2pq = sin⁴θ + 2cos²θ. With u = sin²θ in [0,1], this is u² − 2u + 2 = (u−1)² + 1 ≥ 1, minimum 1 at u = 1 (θ = 90°). The minimum value is 1 — option B.