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

Question

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

(1, $-$3)

($-$1, 3)

($-$1, $-$3)

(1, 3)

Solution

Please login to view the detailed solution steps...

Go to DASH