4cos^4*x-4cos^2*x+1=0

4 * cos^4 x - 4 * cos^2 x + 1 = 0;

Упростим уравнение.

(2 * cos^2 x) ^2 - 2 * (2 * cos^2 x) * 1 + 1^2 = 0;

Разложим на множители.

(2 * cos^2 x - 1) ^2 = 0;

2 * cos^2 x - 1 = 0;

cos^2 x - 1/2 = 0;

(cos x - √2/2) * (cos x + √2/2) = 0;

1) cos x - √2/2 = 0;

cos x = √2/2;

x = + -arccos (√2/2) + 2 * пи * n, n ∈ Z;

x = + -пи/4 + 2 * пи * n, n ∈ Z;

2) cos x + √2/2 = 0;

cos x = - √2/2;

x = + -arccos (-√2/2) + 2 * пи * n, n ∈ Z;

x = + -3 * пи/4 + 2 * пи * n, n ∈ Z.