Предмет: Алгебра, автор: akosh1998

ПОМОГИТЕ
$left { {{x-y= frac{ pi }{2} } atop {sinx+cosy= sqrt{2} }} right.$
$left { {{x-y=- frac{ pi }{2} } atop {cosx+siny=1}} right.$
$left { {x+y= pi } atop {sinx+siny= sqrt{3} }} right.$
$left { {{-x+y= pi } atop {cosx-cosy=1}} right.$

Ответы

Автор ответа: NNNLLL54

$1); left { {{x=y+frac{pi}{2}} atop {sin(frac{pi}{2}+y)+cosy=sqrt2}} right. ; left { {{x=y+frac{pi}{2}} atop {cosy+cosy=sqrt2}} right. ; left { {{x=y+frac{pi}{2}} atop {2cosy=sqrt2}} right. \\cosy=frac{sqrt2}{2},; y=pm frac{pi}{4}+2pi n,; nin Z\\x=frac{pi}{2}pm frac{pi}{4}+2pi n,; nin Z\\ Otvet:left { {{y=frac{pi}{4}+2pi n} atop {x=frac{3pi}{4}+2pi n}} right. ; ili; left { {{y=-frac{pi}{4}+2pi n} atop {x=frac{pi}{4}+2pi n}} right.$

$3); left { {{x=pi -y} atop {sin(pi -y)+siny=sqrt3}} right. ; left { {{x=pi -y} atop {2siny=sqrt3}} right. \\siny=frac{sqrt3}{2},; y=(-1)^{n}frac{pi}{3}+pi n,; nin Z\\x=pi -(-1)^{n}frac{pi}{3}+pi n\\ Otvet:; left { {{y=frac{pi}{3}+2pi n} atop {x=frac{2pi }{3}+2pi n}} right. ; ili; left { {{y=frac{2pi }{3}+2pi n} atop {x=frac{pi}{3}+2pi n}} right.$