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