Cos4x+cos2x=0

√3 sin3x+cos3x=1

4x = 1 - 2 sin^2 2x;

4 sin^4 2x + 3 (1 - 2 sin^2 2x) - 1 = 0;

4 sin^4 2x + 3 - 6 sin^ 2x - 1 = 0;

4 sin^4 2x - 6 sin^2 2x + 2 = 0;

2 sin^4 2x - 3 sin^2 2x + 1 = 0;

sin^2 2x = t; - 1 ≤ t ≤ 1;

2 t^2 - 3 t + 1 = 0;

t1 = 1; ⇒ sin^2 2x = 1; ⇒ sin 2x = + - 1; ⇒ 2x = pi/2 + pi*k; ⇒ x = pi + 2 pi*k.

t2 = 1/2; ⇒ sin^2 2x = 1/2; ⇒sin 2x = + - sgrt2/2; 2x = pi/4 + pik/2; ⇒x = pi/2 + pik; k-Z.

б) x = pi; 3 pi/2.

2x=a

cos (2a) + cos (a) = 0

cosˆ2 (a) - sinˆ2 (a) + cos (a) = 0

2cosˆ2 (a) - 1+cos (a) = 0

cos (a) = x

2xˆ2+x-1=0

D=1+8=9

x=cos (a) = (-1+/-3) / 4=-1; 1/2

cos (a) = - 1

cos (a) = 1/2

a=Pi+2*Pi*n

2x=Pi+2*Pi*n

x=Pi/2+Pi*n

cos (a) = 1/2

2x=a=Pi/3+2Pi*n

x=Pi/6+Pi*n

2) sqrt (3) * sin3x+cos3x=1

2 * (1/2 * sqrt (3) * sin3x + 1/2*cos3x) = 1

2 * (sin (pi/6) * cos3x+cos (pi/6) * sin3x) = 1

2 * (sin (3x+Pi/6)) = 1

sin (3x+Pi/6) = 1/2

3x+Pi/6=Pi/6+2Pi*n

3x=2Pi*n

x=2Pi*n/3