If alpha = lim(x rarr pi//4)""(tan^(3)x ...

If `alpha = lim_(x rarr pi//4)""(tan^(3)x - tan x)/(cos (x + (pi)/(4)))` and `beta = lim_(x rarr 0)(cos x)^(cot x)` are the roots of the equation, `a x^(2) + bx -4 = 0`, then the ordered pair (a, b) is :

A

`(1, -3)`

B

`(-1, 3)`

C

`(1, 3)`

D

`(-1, -3)`

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