If α = lim x → (π)/4 (tan ³x - tan x)/(cos (x + (π)/4)) and β = lim x → 0 (cos x)^(cot x) are the roots of the equation, ax² + bx - 4 = 0, then the ordered pair (a, b) is:

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 31 Aug, Evening shift · Q4288

JEE Main 202131 Aug, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

\alpha = \mathop {\lim }\limits_{x \to {\pi \over 4}} {{{{\tan }^3}x - \tan x} \over {\cos \left( {x + {\pi \over 4}} \right)}}

and

\beta = \mathop {\lim }\limits_{x \to 0 } {(\cos x)^{\cot x}}

are the roots of the equation, ax² + bx

-

4 = 0, then the ordered pair (a, b) is :

JEE Main 2021 · 31 Aug, Evening shift · Q4288

JEE Main 202131 Aug, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

\alpha = \mathop {\lim }\limits_{x \to {\pi \over 4}} {{{{\tan }^3}x - \tan x} \over {\cos \left( {x + {\pi \over 4}} \right)}}

and

\beta = \mathop {\lim }\limits_{x \to 0 } {(\cos x)^{\cot x}}

are the roots of the equation, ax² + bx

-

4 = 0, then the ordered pair (a, b) is :