Решите систему:

x + y = pi/3;

sin (x) * sin (y) = 1/4

X = π/3 - y

sin (π/3 - y) * siny = 1/4

(sin (π/3) * cosy - siny*cos (π/3)) * siny = 1/4

((cosy) * √3/2 - (siny) / 2) * siny = 1/4

(cosy*siny*√3 - sin^2 (y)) / 2 = 1/4

√3*cosy*siny - sin^2 (y) = 1/2

1/2 = 0.5sin^2 (y) + 0.5cos^2 (y)

√3*cosy*siny - sin^2 (y) - 0.5sin^2 (y) - 0.5cos^2 (y) = 0 - делим на - 0.5

cos^2 (y) + 3sin^2 (y) - 2√3*cosy*siny = 0 - делим на cos^2 (y)

1 + 3tg^2 (y) - 2√3*tgy = 0

замена tg (y) = t

3t^2 - 2√3*t + 1 = 0

(√3t - 1) ^2 = 0

√3t = 1, t = √3/3

tg (y) = √3/3

y = π/3 + πk

x = π/3 - π/3 - πk = - πk

Ответ: x = - πk, y = π/3 + πk