X+У=π/3, y=
π/3 -x
sinx·siny=1/4
sinx·sin(
π/3-x)=0,5cos(x-(
π/3-x)-
-cos(x+
π/3-x)=1/4
0,5(cos(2x-( π/3)-cos(
π/3) )=1/4
0,5
cos(2x-( π/3) -0,25=0,25,
0,5 cos(2x-( π/3)=0,5, cos(2x-( π/3)=1
2x-
π/3 = 2πn,2x=2πn+
π/3 ,
x=
πn
+ π/6,y=
π/3- πn -
π/6=
π/6 - πn
Ответ(
πn + π/6 ;
π/6 - πn),где
n целое число.