Question

sinx +cos x = корень из 2

Answer 1

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