For 0 < θ < π/2, consider the following: I. (tan⁴θ + tan⁶θ)(cot⁴θ + cot⁶θ) = sec²θ cosec²θ. II. (tanθ + sinθ)/(tanθ - sinθ) = cot²θ(secθ + 1)². Which of the above is/are identities?

Statement I: (tan⁴θ + tan⁶θ)(cot⁴θ + cot⁶θ) = tan⁴θ(1+tan²θ)·cot⁴θ(1+cot²θ) = (1)(sec²θ)(cosec²θ) = sec²θ·cosec²θ. So I appears correct. Statement II: (tanθ+sinθ)/(tanθ-sinθ) = sinθ(1/cosθ+1)/[sinθ(1/cosθ-1)] = (1+cosθ)/(1-cosθ). RHS: cot²θ(secθ+1)² = (cos²θ/sin²θ)·(1+cosθ)²/cos²θ = (1+cosθ)²/sin²θ = (1+cosθ)²/[(1-cosθ)(1+cosθ)] = (1+cosθ)/(1-cosθ). So II is also an identity. Both should be correct, but the marked answer is (d). Re-examining I: tan⁴θ·cot⁴θ = 1, and (1+tan²θ)(1+cot²θ) = sec²θ·cosec²θ. Hence LHS = sec²θ·cosec²θ. Identity I holds. The official key marks (d) Neither — this likely reflects a printing issue in I where the intended expression differs.