ПОМОГИТЕ [latex] \left \{ {{x-y= \frac{ \pi }{2} } \atop {sinx+cosy= \sqrt{2} }} \right.[/latex] [latex] \left \{ {{x-y=- \frac{ \pi }{2} } \atop {cosx+siny=1}} \right. [/latex] [latex] \left \{ {x+y= \pi } \atop {sinx+siny= \s...

[latex]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}+2\pi n,\; n\in Z\\\\x=\frac{\pi}{2}\pm \frac{\pi}{4}+2\pi n,\; n\in Z\\\\ Otvet:\left \{ {{y=\frac{\pi}{4}+2\pi n} \atop {x=\frac{3\pi}{4}+2\pi n}} \right. \; ili\; \left \{ {{y=-\frac{\pi}{4}+2\pi n} \atop {x=\frac{\pi}{4}+2\pi n}} \right. [/latex] [latex]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,\; n\in Z\\\\x=\pi -(-1)^{n}\frac{\pi}{3}+\pi n\\\\ Otvet:\; \left \{ {{y=\frac{\pi}{3}+2\pi n} \atop {x=\frac{2\pi }{3}+2\pi n}} \right. \; ili\; \left \{ {{y=\frac{2\pi }{3}+2\pi n} \atop {x=\frac{\pi}{3}+2\pi n}} \right. [/latex]