Question

Решите уравнение.
$\sqrt{2}sin2x+(2-\sqrt{2}cos2x-\sqrt{2}sin2x)=2+\sqrt{2}$

Answer 1

$\sqrt{2}Sin2x+(2-\sqrt{2} Cos2x-\sqrt{2}Sin2x)=2+\sqrt{2}\\\\\sqrt{2}Sin2x+2-\sqrt{2} Cos2x-\sqrt{2}Sin2x=2+\sqrt{2}\\\\2-\sqrt{2} Cos2x=2+\sqrt{2}\\\\\sqrt{2}Cos2x=2-2-\sqrt{2}\\\\\sqrt{2}Cos2x=-\sqrt{2}\\\\Cos2x=-1\\\\2x=\pi+2\pi n,n \in Z\\\\\boxed{x=\frac{\pi }{2}+\pi n,n\in Z}$