а)1+ cos 4x = cos 2x 2cos²2x=cos2x 2cos²2x-cos2x=0 cos2x(2cos2x-1)=0 cos2x=0 2x=π/2+πk x=π/4+πk/2,k∈z 2cos2x-1=0 cos2x=1/2 2x=-π/3+2πk U 2x=π/3+2πk x=-π/6+πk U x=π/6+πk,k∈z ответ x={π/4+πk/2;-π/6+πk;π/6+πk,k∈z}
б)4sin^2 x - 4sin x + 1 = 0 (2sinx-1)²=0 2sinx-1=0 sinx=1/2 x=(-1)^k*π/6+πk,k∈z
1+cos4x=cos2x
2cos²2x=cos2x
cos2x(2cos2x-1)=0
cos2x=0
2x=π/2+πk
x=π/4+πk/2
cos2x=1/2
2x=±π/3+2πk
x=±π/6+πk
ответ: x=π/4+πk/2, x=±π/6+πk; k∈Z
б)
4sin²x-4sinx+1=0
(2sinx-1)²=0
sinx=1/2
x=π/6+2πk, x=5π/6+2πk
ответ: x=π/6+2πk, x=5π/6+2πk; k∈Z
2cos²2x=cos2x
2cos²2x-cos2x=0
cos2x(2cos2x-1)=0
cos2x=0
2x=π/2+πk
x=π/4+πk/2,k∈z
2cos2x-1=0
cos2x=1/2
2x=-π/3+2πk U 2x=π/3+2πk
x=-π/6+πk U x=π/6+πk,k∈z
ответ x={π/4+πk/2;-π/6+πk;π/6+πk,k∈z}
б)4sin^2 x - 4sin x + 1 = 0
(2sinx-1)²=0
2sinx-1=0
sinx=1/2
x=(-1)^k*π/6+πk,k∈z