Question

Решить систему уравнений

Answer 1

$\displaystyle\bf\\\left \{ {{Cos(x-y)=0} \atop {Sin(x+y)=1}} \right. \\\\\\+\left \{ {{x-y=\frac{\pi }{2} +\pi n,n\in Z} \atop {x+y=\frac{\pi }{2} +2\pi n,n\in Z}} \right. \\-------------\\2x=\pi +3\pi n,n\in Z\\\\x=\frac{\pi }{2} +\frac{3\pi n}{2} ,n\in Z\\\\y=x-\frac{\pi }{2} -\pi n=\frac{\pi }{2} +\frac{3\pi n}{2} -\frac{\pi }{2} -\pi n=\frac{\pi n}{2} ,n\in Z\\\\Otvet:\Big(\frac{\pi }{2} +\frac{3\pi n}{2} \ ; \ \frac{\pi n}{2} \Big),n\in Z$