hello! who can solve that without using Lhopitals rule
thank you
Another approach :
$\displaystyle
\frac{x(1-\tan (x))}{\cos(2x)}=-x\cdot \frac{\tan (x
)-\tan\left(\pi/4 \right)}{x-\frac{\pi}{4}}\cdot \frac{x-\frac{\pi}{4}}{\cos(2x)-\cos(2\pi/4)}$
Now recall that $\displaystyle \lim_{x\to a}\frac{f(x)-f(a)}{x-a}=f'(a)$ and you are done.