Explanation

M = sinθ·cosθ = (1/2)sin 2θ, so M + N = M + M² is a quadratic in M opening upward, whose unconstrained minimum is at M = −1/2 with value (−1/2)(1/2) = −0.25. Since sin 2θ ranges over [−1, 1], M ranges over [−1/2, 1/2], and the endpoint M = −1/2 is attained (when sin 2θ = −1). Hence the minimum value of M + N is −0.25, option (a).