Ответ:
Объяснение:
\left \{ {{x=\frac{\pi}{2}-y} \atop {sin(\frac{\pi}{2}-y)+cos(y)=\sqrt{2} }} \right. <=>\left \{ {{x=\frac{\pi}{2}-y} \atop {cos(y)=\frac{\sqrt{2} }{2} }} \right. \\y=\frac{\pi}{4}+2\pik\\ x=\frac{7\pi}{4}+2\pik\\ x=\frac{\pi}{4}\\ x=-\frac{5\pi}{4}" alt="\left \{ {{x+y=\frac{\pi}{2} } \atop {sin(x)+cos(y)=\sqrt{2} }} \right. <=>\left \{ {{x=\frac{\pi}{2}-y} \atop {sin(\frac{\pi}{2}-y)+cos(y)=\sqrt{2} }} \right. <=>\left \{ {{x=\frac{\pi}{2}-y} \atop {cos(y)=\frac{\sqrt{2} }{2} }} \right. \\y=\frac{\pi}{4}+2\pik\\ x=\frac{7\pi}{4}+2\pik\\ x=\frac{\pi}{4}\\ x=-\frac{5\pi}{4}" align="absmiddle" class="latex-formula">