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) + k, 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 = -/6 + 2k, k Z;
• x = -5/6 + 2k, k Z;

   2) sinx = (1 + 3)/4 = 4/4 = 1;

      x = /2 + 2k, 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 = /2 + k, k Z;
  [2x = -arcsin(1/4) + 2k, k Z;
  [2x = - + arcsin(1/4) + 2k, k Z;
• [x = /4 + k/2, k Z;
  [x = -1/2arcsin(1/4) + k, k Z;
  [2x = -/2 + 1/2arcsin(1/4) + k, k Z.