Найти предел: \(
\lim_{x\to\frac{\pi}{4}}\large \frac{1-\tan{x}}{\cos{2x}}
\)

Решение

\( \displaylines{
\lim_{x\to\frac{\pi}{4}} \frac{1-\tan{x}}{\cos{2x}}
= \lim_{x\to\frac{\pi}{4}} \frac{ -\frac{1}{\cos^2{x}} }{ -2\sin{x} }
= \lim_{x\to\frac{\pi}{4}} \frac{1}{2\sin{2x}\cos^2{x}}
= 1
}\)

Ответ: \(1\).