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 + π/2) - sin6x) = 0;
• cos3x(sin6x - sin(x + π/2)) = 0;
• cos3x * 2sin(5x/2 - π/4) * cos(7x/2 + π/4) = 0.

   2. Приравняем к нулю каждый из множителей:

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

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