2√2cos(x) +2 - cos (2x)=0
2√2cos(x) +2 - (2cos²(x) - 1)=0
2√2cos(x) +2 - 2cos²(x) +1=0
2√2cos(x) + 3 - 2cos²(x) =0
2cos²(x) - 2√2cos(x) -3 =0 cos(x)=a
2a² - (2√2)a -3=0
D=8+24=32 √D=4√2
a=(2√2 + 4√2)/4=6√2 /4= (3√2) /2 cos(x) =(3√2) /2 >1 нет решения
a=(2√2 - 4√2)/4= -2√2/4=(-√2)/2 cos(x) = (- √2 )/2
cos(x) =
(- √2 )/2
х= arccos √ 2/2+2 πn, n∈ z
x=
±3π/4+2 πn, где n∈ z
х=3π/4+2πn и х=5π/4 +2πn
5π ≤ 3π/4+2πn ≤ 13π/2
17π/4 ≤ 2 πn ≤ 23π/4
17/8 ≤ n ≤ 23/8 n∈ z
n=2 3π/4+4π = 19π/4
5π ≤ 5π/4+2πn ≤ 13π/2
15π/4 ≤
2 πn ≤ 21π/4
15/8 ≤ n ≤ 21/8 n∈ z
1 ≤
n ≤
2
n=2 5π/4+4π = 21π/4
n=1 5π/4+2π = 13π/4
Ответ : 13π/4 19π/4 ; 21π/4