Question

2 sin (x-(pi/4))= корень из 2

Answer 1

$2sin(x-\frac{\pi}4)=\sqrt2\\sin(x-\frac{\pi}4)=\frac{\sqrt2}2\\\\ \left[\begin{array}{ccc}x-\frac{\pi}4=\frac{\pi}4+2\pi n;n\in Z\\\\x-\frac{\pi}4=\frac{3\pi}4+2\pi n;n\in Z\end{array}\right=\ \textgreater \ \left[\begin{array}{ccc}x=\frac{\pi}2+2\pi n;n\in Z\\\\x=\pi+2\pi n;n\in Z\end{array}\right$