Explanation

Factor sinθ from the numerator and cosθ from the denominator: sinθ(1−2sin²θ) / (cosθ(2cos²θ−1)). The double-angle identities give 1−2sin²θ = cos2θ and 2cos²θ−1 = cos2θ, so the cos2θ factors cancel. What remains is sinθ/cosθ = tanθ — option D.