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?

For I: tan⁴θ + tan⁶θ = tan⁴θ(1 + tan²θ) = tan⁴θ·sec²θ; cot⁴θ + cot⁶θ = cot⁴θ(1 + cot²θ) = cot⁴θ·cosec²θ. Their product = tan⁴θ·cot⁴θ·sec²θ·cosec²θ = sec²θ·cosec²θ — this is correct. Wait, re-checking: tan⁴θ·cot⁴θ = 1, so I gives sec²θ·cosec²θ. So I is an identity. For II: (tanθ + sinθ)/(tanθ − sinθ) = sinθ(1/cosθ + 1)/sinθ(1/cosθ − 1) = (1 + cosθ)/(1 − cosθ). Also 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 are identities, answer is (c) Both I and II.