Lim (x стремится к П/2) 1+cos 2x / cos x

[latex]\displaystyle\lim_{x\to\frac{\pi}{2}}\frac{1+\cos2x}{\cos{x}} = \lim_{x\to\frac{\pi}{2}} \frac{2\cos^2x}{\cos{x}} = \\\\ = 2\lim_{x\to\frac{\pi}{2}}\cos{x} = 2\cdot0 = 0[/latex]