Question

sinx +cos x = корень из 2

Answer 1

$sinx + cosx= \sqrt{2} \\ \frac{1}{ \sqrt{2} } cosx - \frac{1}{ \sqrt{2} }x=-1 \\ cos \frac{\pi}{4}cosx-sin \frac{\pi}{4}sinx=-1 \\ cos(\frac{\pi}{4}+x)=-1 \\ \frac{\pi}{4} +x=arccos(-1)+2\pi n \ \ \ \ \ \boxed{n \in Z} \\ \frac{\pi}{4} +x = \pi + 2\pi n \ \ \ \ \ \boxed{n \in Z} \\ x = \frac{3 \pi}{4} + 2\pi n \ \ \ \ \ \boxed{n \in Z}$