1) 2sin^2x-5cosx-1=0 2) sin2x-3cos2x=0 3) 3cos^2x-sin^2x+4sinx*cosx=0

   1)

• 2sin^2x - 5cosx - 1 = 0;
• 2 - 2cos^2x - 5cosx - 1 = 0;
• 2cos^2x + 5cosx - 1 = 0;
• cosx = (-5 (5^2 + 4 * 2))/4 = (-5 33)/4;
• a) cosx = (-5 - 33)/4 lt; -1 - нет решения;
• b) cosx = (-5 + 33)/4 = (33 - 5)/4;
• x = arccos((33 - 5)/4) + 2k, k Z.

   2)

• sin2x - 3cos2x = 0;
• sin2x = 3cos2x;
• tg2x = 3;
• 2x = /3 + k, k Z;
• x = /6 + k/2, k Z.

   3)

• 3cos^2x - sin^2x + 4sinx * cosx = 0;
• 3(1 + cos2x)/2 - (1 - cos2x)/2 + 4sinx * cosx = 0;
• 1 + 2cos2x + 2sin2x = 0;
• 2(cos2x + sin2x) = -1;
• cos2x + sin2x = -1/2;
• 2/2 * (cos2x + sin2x) = -1/2 * 2/2;
• sin(2x + /4) = -2/4;

• [2x + /4 = -arcsin(2/4) + 2k, k Z;
  [2x + /4 = + arcsin(2/4) + 2k, k Z;
• [2x = -/4 - arcsin(2/4) + 2k, k Z;
  [2x = -/4 + + arcsin(2/4) + 2k, k Z;
• [x = -/8 - 1/2arcsin(2/4) + k, k Z;
  [x = 3/8 + 1/2arcsin(2/4) + k, k Z.