$\lim\limits_{x \rightarrow \pi / 4} \frac{cosec ~x-\sec x}{\cot x-\tan x}$
Answer & explanation
Correct answer: option 2
$\lim\limits_{x \rightarrow \frac{\pi}{4}} \frac{cosec ~x-\sec x}{\cot x-\tan x}=\lim\limits_{x \rightarrow \frac{\pi}{4}} \frac{1}{\sin x+\cos x}= 1/\sqrt{2}$
Hence (2) is the correct answer.