1)x=π/6+y
cos(π/6+y)*siny=1/4
1/2(sin(π/6+y-y)+sin(π/6+y+y))=1/4
1/2(sinπ/6)+sin(π/6+2y))=1/4
1/2*1/2+1/2sin(π/6+2y)=1/4
1/2sin(π/6+2y)=0
π/6+2y=πn⇒x=-π/12+πn
x=π/6-π/12+πn=π/12+πn
2)y=5π/2-x
cos2x+sin(5π/2-x)=2
cos2x+cosx=2
2cos²x-1+cosx-2=0
cosx=a
2a²+a-3=0
D=1+24=25
a1=(-1-5)/4=-1,5⇒cosx=-1,5 нет решения
a2=(-1+5)/4=1⇒cosx=1⇒x=2πn
y=5π/2+2πn