[tex] \lim_{x \to \ \frac{1}{4} \pi} \frac{tan x - cot x}{x - \frac{ \pi }{4} } [/tex]

Lim (Tan x - cot x)/(x - π/4)
x=>π/4

Lim ((sin x)/(cos x) - (cos x)/(sin x)) / (x - π/4)
x=>π/4

Lim ((sin^2 x - cos^2 x)/(sin x cos x)) / (x - π/4)
x=>π/4

Lim (- cos 2x) / (x - π/4)(sin x cos x)
x=>π/4

Lim (- sin (π/2 - 2x)) / (x - π/4)(sin x cos x)
x=>π/4

Lim (sin (2x - π/2)) / (x - π/4)(sin x cos x)
x=>π/4

Lim (sin 2(x - π/4))/(x - π/4) . 1/(sin x cos x)
x=>π/4

= 2 . 1/(sin π/4 cos π/4)
= 2 . 1/(1/2 √2 . 1/2 √2)
= 2 . 1/(1/2)
= 2 . 2
= 4