Sinx+cosx=корень из 2/2

[latex] \sqrt{2} sin(x+\phi)= \frac{ \sqrt{2} }{2} ,\ tg\ \phi = \frac{1}{1} =1\\ sin(x+\phi)= \frac{ 1}{2}\\ x+\phi = (-1)^{n} \frac{ \pi }{6}+ \pi n,\ n \in Z\\ x=(-1)^{n} \frac{ \pi }{6}-arctg1+ \pi n,\ n \in Z\\ x=(-1)^{n} \frac{ \pi }{6}-\frac{ \pi }{4}+ \pi n,\ n \in Z.[/latex]