If α = lim x → π / 4 tan 3 x - tan x cos x + π 4 and β = lim x → 0 cos x cot x are the roots of the equation, a x 2 + b x - 4 = 0 , then the ordered pair a , b is :

Step-by-step solution

If, β = lim x → 0 cos x cot x ( 1 ∞     form) β = e   lim   x → 0 cot x cos x - 1 β = e   lim x → 0 - cos x sin x 1 - 1 + 2 sin 2 x 2 β = e   lim x → 0   - cos x 2 sin x 2 . cos x 2 1 - 1 + 2 sin 2 x 2 β = e   lim x → 0   - cos x . sin x 2 cos x 2 β = e 0 β = 1 α = lim x → π / 4 tan 3 x - tan x cos x + π 4 = lim x → π / 4 tan x ( tan x + 1 ) ( tan x - 1 ) cos x + π