Let - π 6 < θ < - π 12 . Suppose α 1 and β 1 are the roots of the equation x 2 - 2 x sec ⁡ θ + 1 = 0 and α 2 and β 2 are the roots of the equation x 2 + 2 x tan ⁡ θ - 1 = 0 . If α 1 > β 1 and α 2 > β 2 , then α 1 + β 2 equals

Step-by-step solution

As α 1 > β 1 so ' +' sign will be used for α 1 , β 2 < α 2 so ' -' sign for β 2 . α 1 = 2 sec   θ ±   4 sec 2   θ - 4 2 , β 2 = - 2 tan   θ  -   4 tan 2   θ + 4 2 α 1 = sec   θ + tan   θ β 2 =   - tan   θ - sec   θ α 1 = sec   θ - tan   θ   ∵       θ ∈ - π 6 ,   - &#96