3sin²(3x)+10sin(3x)cos(3x)+3cos²(3x)=0

3sin^2(3x) + 10*sin(3x)*cos(3x) + 3cos^2(3x) = 0 // ÷  cos^2(3x) ≠ 0 3tg^2(3x) + 10tg(3x) + 3 = 0  Пусть tg(3x) = t ==>  3t^2 + 10t + 3 = 0  D = 100 - 4*9 = 64  t1 = ( - 10 + 8)/6 = - 1/3 t2 = ( - 10 - 8)/6 = - 3  tg(3x) = - 1/3 3x = - arctg(1/3) + pik x = - 1/3*arctg(1/3) + pik/3, k ∈ Z tg(3x) = - 3  3x = - arctg(3) + pik x =  - 1/3*arctg(3) + pik/3, k∈ Z