Question

Решите неравенство:
а) 2cos x - √2 > 0

Answer 1

$2cos(x)- \sqrt{2}\ \textgreater \ 0 \\ \\ 2cos(x)\ \textgreater \ \sqrt{2} \\ \\ cos(x)\ \textgreater \ \frac{ \sqrt{2} }{2}$

Первая точка $\frac{ \sqrt{2} }{2} = \frac{\pi}{4}$

Вторая точка $2\pi- \frac{\pi}{4}= \frac{7\pi}{4}$

Ответ: $x\in [ \frac{\pi}{4}+2\pi n; \frac{7\pi}{4} +2\pi n ] , n\in Z$