Решите систему:

X+У=pi/3

sinx*siny=1/4

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.