Explanation

Put t = cos θ ∈ (0, 1]; then cos³θ + sec³θ = t³ + 1/t³. By AM–GM, t³ + 1/t³ ≥ 2√(t³·1/t³) = 2, with equality at t = 1, i.e. θ = 0°, which is allowed. The minimum value is 2, option (c).