Question

2cos2(x+π/6)-3cos(x+π/6)+1=0

Answer 1

2cos²(x+π/6)-3cos(x+π/6)+1=0
Замена переменной:
cos(x+π/6)=t, решаем квадратное уравнение
2t²-3t+1=0
D=(-3)²-4·2=1
t=(3-1)/4=1/2  или  t=(3+1)/4=1
cos(x+π/6)=1/2      или      сos(x+π/6)=1;
x+π/6=±arccos(1/2) +2πk, k∈Z  или  x+π/6=arccos1+2π n, n∈Z;   
x+π/6=±π/3 +2πk, k∈Z  или  x+π/6=0+2π n, n∈Z;   
x=±π/3 -π/6+2πk, k∈Z  или  x=-π/6+2π n, n∈Z;
О т в е т. ±π/3 -π/6+2πk,=-π/6+2π n, k, n∈Z.