If α and β are roots of the equation x 2 + 5 x - 6 = 0 then the value of tan - 1 ⁡ α - tan - 1 ⁡ β is

Step-by-step solution

x 2 + 5 x - 6 = 0 x 2 + 5 x - 6 = 0 x 2 + 6 x - x - 6 = 0 x x + 6 - 1 x + 6 = 0 x - 1 x + 6 = 0 x = 1, nbsp; x ≠ - 6 (Since modulus can not be giving negative values) ∴ x = 1 ∴ x = ± 1 α = 1 , β = - 1 ∴ tan - 1 ⁡ α - tan - 1 ⁡ β = tan - 1 ⁡ 1 - tan - 1 ⁡ - 1 = π 4 - - π 4 = π 2 = π 2