Question

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

Answer 1

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