Question

tg(x-пи/8)>0 решите, пожалуйста ​

Answer 1

$\mathrm{tg}\left ( x-\cfrac{\pi}{8} \right )\Leftrightarrow \begin{cases}x-\cfrac{\pi}{8} > 0+\pi k\\ x-\cfrac{\pi}{8} < \cfrac{\pi}{2}+\pi k\end{cases}, \; k\in\mathbb{Z}\Rightarrow x\in\left ( \frac{\pi}{8}+\pi k,\frac{5\pi }{8}+\pi k \right ), \; k\in\mathbb{Z}$