Cos^2(3x) + cos^2(4x) + cos^2(5x) = 3/2

   1. Умножим обе доли уравнения на 2:

• cos^2(3x) + cos^2(4x) + cos^2(5x) = 3/2;
• 2cos^2(3x) + 2cos^2(4x) + 2cos^2(5x) = 3;
• 2cos^2(3x) - 1 + 2cos^2(4x) - 1 + 2cos^2(5x) - 1 = 0.

   2. Косинус двойного угла и сумма косинусов:

• cos6x + cos8x + cos10x = 0;
• 2cos((10x + 6x)/2) * cos((10x - 6x)/2) + cos8x = 0;
• 2cos8x * cos2x + cos8x = 0;
• cos8x(2cos2x + 1) = 0;

• [cos8x = 0;
  [2cos2x + 1 = 0;
• [cos8x = 0;
  [cos2x = -1/2;
• [8x = /2 + k, k Z;
  [2x = 2/3 + 2k, k Z;
• [x = /16 + k/8, k Z;
  [x = /3 + k, k Z.

   Ответ: /16 + k/8; /3 + k, k Z.