Question

& sin (2x-П/4)+1=0
7​

Answer 1

$\sin \left (2x - \dfrac{\pi}{4} \right)+ 1 = 0$

$\sin \left (2x - \dfrac{\pi}{4} \right) = -1$

$2x - \dfrac{\pi}{4} = -\dfrac{\pi}{2} + 2\pi n, \ n \in \mathbb{Z}$

$2x= \dfrac{\pi}{4} - \dfrac{\pi}{2} + 2\pi n, \ n \in \mathbb{Z}$

$2x = -\dfrac{\pi}{4} + 2\pi n, \ n \in \mathbb{Z} \ \ \ | : 2$

$x = -\dfrac{\pi}{8} + \pi n, \ n \in \mathbb{Z}$

Ответ: $x = -\dfrac{\pi}{8} + \pi n, \ n \in \mathbb{Z}$