Question

cos (3x+π/4)=корень2/2

Answer 1

$\cos(3x + \frac{\pi}{4} ) = \frac{ \sqrt{2} }{2} \\ 3x + \frac{\pi}{4} = \pm \frac{\pi}{4} + 2\pi n \\ \left[ \begin{gathered} 3x = \frac{\pi}{4} - \frac{\pi}{4} + 2\pi n \\ 3x = -\frac{\pi}{4}-\frac{\pi}{4}+2\pi n \end{gathered} \right. \\ \left[ \begin{gathered} x = \frac{2\pi}{3} n \\ x = -\frac{\pi}{6}+ \frac{2\pi}{3} n, \: n \in Z \end{gathered} \right.$