1) cos7x+ cosx=02) sinx- 3sinxcosx+2cosx=03) 1+cosx+cos2x=0

   1. Сумма косинусов:

• cos7x + cosx = 0;
• 2cos((7x + x)/2) * cos((7x - x)/2) = 0;
• 2cos4x * cos3x = 0;

• [cos4x = 0;
  [cos3x = 0;
• [4x = /2 + k, k Z;
  [3x = /2 + k, k Z;
• [x = /8 + k/4, k Z;
  [x = /6 + k/3, k Z.

   2.

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

   1) tgx = (3 - 1)/2 = 1;

      x = /4 + k, k Z.

   2) tgx = (3 + 1)/2 = 2;

      x = arctg2 + k, k Z.

   3.

• 1 + cosx + cos2x = 0;
• cosx + 2cos^2x = 0;
• cosx(1 + 2cosx) = 0;

• [cosx = 0;
  [1 + 2cosx = 0;
• [cosx = 0;
  [cosx = -1/2;
• [x = /2 + k, k Z;
  [x = 2/3 + 2k, k Z.