Question

помогите алгебра 10 класс 25 балов​

Answer 1

$\displaystyle\left \{ {{x+y=\pi /2} \atop {sin(x)+cos(y)=\sqrt{2}}} \right. \\\\\left \{ {{x=\pi /2-y} \atop {sin(\pi /2-y)+cos(y)=\sqrt{2}}} \right. \\\\cos(y)+cos(y)=\sqrt{2}\\\\2cos(y)=\sqrt{2}\\\\cos(y)=\frac{\sqrt{2}}{2}\\\\y=\pm \frac{\pi }{4}+2\pi n; n \in Z\\\\y_1=\frac{\pi }{4}+2\pi n; x_1=\frac{\pi }{2}-\frac{\pi }{4}-2\pi n= \frac{\pi }{4}-2\pi n; n \in Z\\\\y_2= -\frac{\pi }{4}+2\pi n; x_2=\frac{\pi }{2}+\frac{\pi }{4}-2\pi n=\frac{3\pi }{4}-2\pi n; n \in Z$

ответ : ( π/4 +2πn; π/4-2πn) или (3π/4+2πn; -π/4-2πn)