limx→π/41-cot3x2-cotx-cot3x is

$\lim_{x \to π / 4} \frac{1 - \cot^{3} x}{2 - \cot x - \cot^{3} x}$ is

A
11/4
B
3/4
C
1/2
D
none of these

Solution:

$\lim_{x \to π / 4} \frac{1 - \cot^{3} x}{2 - \cot x - \cot^{3} x}$

$= \lim_{x \to π / 4} \frac{(1 - \cot x) (1 + \cot x + \cot^{2} x)}{(1 - \cot x) (\cot^{2} x + \cot x + 2)}$

$= \lim_{x \to π / 4} \frac{1 + \cot x + \cot^{2} x}{\cot^{2} x + \cot x + 2} = \frac{3}{4}$

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