sin x*cos y=0
cos x*sin y=-1

Можно так 
[tex] \left \{ {{sinxcosy=0} \atop {cosxsiny=-1}} \right. \left \{ {{sinxcosy+cosxsiny=-1} \atop {sinxcosy-cosxsiny=1}} \right. \left \{ {{sin(x+y)=-1} \atop {sin(x-y)=1}} \right.\left \{ {{x+y=- \frac{ \pi }{2}+2 \pi n,n \in Z } \atop {x-y=\frac{ \pi }{2}+2 \pi n,n \in Z }} \right. [/tex]
[tex]\left \{ {{2x=4 \pi n,n \in Z } \atop {2y=- \pi }} \right. \left \{ {{x=2 \pi n,n \in Z } \atop {y=- \frac{ \pi }{2} }} \right. [/tex]