34sinx=cosx (2cos^2) x=1-sinx 2sin4x - (2sin^2) x=1

1.

4sinx = cosx; 4sinx/cosx = 1; 4tgx = 1; tgx = 1/4; x = arctg (1/4) + πk, k ∈ Z.

2.

2cos^2x = 1 - sinx; 2 - 2sin^2x - 1 + sinx = 0; - 2sin^2x + sinx + 1 = 0; 2sin^2x - sinx - 1 = 0; D = 1 + 4 * 2 = 9; sinx = (1 ± √9) / 4 = (1 ± 3) / 4;

1) sinx = (1 - 3) / 4 = - 2/4 = - 1/2;

x = - π/6 + 2πk, k ∈ Z; x = - 5π/6 + 2πk, k ∈ Z;

2) sinx = (1 + 3) / 4 = 4/4 = 1;

x = π/2 + 2πk, k ∈ Z.

3.

2sin4x - 2sin^2x + 1 = 0; 4sin2x * cos2x + cos2x = 0; cos2x (4sin2x + 1) = 0; [cos2x = 0;

[4sin2x + 1 = 0; [cos2x = 0;

[sin2x = - 1/4; [2x = π/2 + πk, k ∈ Z;

[2x = - arcsin (1/4) + 2πk, k ∈ Z;

[2x = - π + arcsin (1/4) + 2πk, k ∈ Z; [x = π/4 + πk/2, k ∈ Z;

[x = - 1/2arcsin (1/4) + πk, k ∈ Z;

[2x = - π/2 + 1/2arcsin (1/4) + πk, k ∈ Z.