cos4x+cos2x=sin9x+sin3x

   1. Воспользуемся тригонометрическими формулами:

• sina + sinb = 2sin((a + b)/2) * cos((a - b)/2);
• sina - sinb = 2sin((a - b)/2) * cos((a + b)/2);
• cosa + cosb = 2cos((a + b)/2) * cos((a - b)/2);

• cos4x + cos2x = sin9x + sin3x;
• 2cos3x * cosx = 2sin6x * cos3x;
• 2cos3x * cosx - 2sin6x * cos3x = 0;
• 2cos3x(cosx - sin6x) = 0;
• 2cos3x(sin(x + /2) - sin6x) = 0;
• cos3x(sin6x - sin(x + /2)) = 0;
• cos3x * 2sin(5x/2 - /4) * cos(7x/2 + /4) = 0.

   2. Приравняем к нулю каждый из множителей:

• [cos3x = 0;
  [sin(5x/2 - /4) = 0;
  [cos(7x/2 + /4) = 0;
• [3x = /2 + k;
  [5x/2 - /4 = k;
  [7x/2 + /4 = /2 + k;
• [x = /6 + k/3;
  [5x = /2 + 2k;
  [7x = /2 + 2k;
• [x = /6 + k/3;
  [x = /10 + 2k/5;
  [x = /14 + 2k/7.

   Ответ: /6 + k/3; /10 + 2k/5; /14 + 2k/7, k Z.