Решить систему тригонометрических уравнений

6x + y = П/4sinx/cosx + siny/cosy = 1 | x,y <> П/2 + Пksinx*cosy + siny*cosx = cosx*cosysin(x+y) = cosx*cosycosx*cosy = sin(П/4)cosx*cos(П/4-x) = sin(П/4)cosx*(cos(П/4)*cos(x) + sin(П/4)*sin(x)) = sin(П/4) | cos(П/4) = sin(П/4)cosx*(cosx+sinx) = 1cos^2x + cosx*sinx = 1cosx*sinx - sin^2x = 0sinx*(cosx - sinx) = 0sinx = 0 -> x = Пk, y = П/4 - Пkcosx = sinx -> x = П/4 - Пk, y = Пk7cos^2x = sinx*sinysin^2x = cosx*cosy1 = sinx*siny + cosx*cosy1 = cos(x-y)x-y = П/2 + 2Пk, y = x + П/2 + 2Пkcos^2x = sinx*sin(x+П/2) = sinx*cosx -> cosx = 0 | cosx = sinxsin^2x = cosx*cos(x+П/2) = cosx*(-sinx) -> sinx = 0 | sinx = -cosx--> cosx = 0 | sinx = 0 --> x = Пn/2, y = П(n+1)/2 + 2Пk8cosx*sqrt(cos2x) = 0 | cos2x >= 02sin^2x = cos(2y-П/3) | 2sin^2x <= 1cosx*sqrt(cos^2x - sin^2x) = 0cosx*sqrt(1 - 2sin^2x) = 0cosx*sqrt(1 - cos(2y-П/3)) = 0cosx = 0 -> x = П/2 + Пk - > 2sin^2x > 1 - не подходитcos(2y-П/3) = 1 - > 2y - П/3 = П/2 + 2Пk -> y = 5П/12 + Пk | cos2x = 1 - 2sin^2x = 1 - cos(2y-П/3) = 0 -> x = П/4 + Пn/2--> x = П/4 + Пn/2, y = 5П/12 + Пk/2