Consider the following statements: I. (cosec α − sec α) is always positive in the first quadrant. II. (tan α − cot α) is always negative in the first quadrant. Which of the statements given above is/are correct?

In the first quadrant (0 < α < π/2): For α = π/3 (60°), cosec 60° = 2/√3 ≈ 1.155 and sec 60° = 2, so cosec − sec = −0.845 (negative). For α = π/6 (30°), cosec − sec = 2 − 2/√3 ≈ 0.845 (positive). So I is false. For tan − cot: at α = π/3, tan = √3, cot = 1/√3, difference = √3 − 1/√3 > 0 (positive). At α = π/6, tan = 1/√3, cot = √3, difference is negative. So II is also false. Neither statement is correct.