Explanation

Since (cosecθ + cotθ)(cosecθ − cotθ) = cosec²θ − cot²θ = 1, we have p = 1/(cosecθ + cotθ) = cosecθ − cotθ = q − cotθ. Then p² − 2pq = (q − cotθ)(−q − cotθ) = −(q² − cot²θ) = −(cosec²θ − cot²θ) = −1, option (a).