Question

решить уравнение sin х + cos х = -√2

Answer 1

$sinx+cosx=-sqrt2|:sqrt2\frac{sqrt2}{2}sinx+cosxfrac{sqrt2}{2}=-1\frac{sqrt2}{2}=cosfrac{pi}{4}, ; frac{sqrt2}{2}=sinfrac{pi}{4}\sinxcosfrac{pi}{4}+cosxsinfrac{pi}{4}=-1\sin(x+frac{pi}{4})=-1\x+frac{pi}{4}=-frac{pi}{2}+2pi n\x=-frac{pi}{4}-frac{pi}{2}+2pi n\x=-frac{3pi}{4}+2pi n, ; nin Z$