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

   1. Умножим обе части 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 = π/2 + πk, k ∈ Z;[2x = ±2π/3 + 2πk, k ∈ Z;
• [x = π/16 + πk/8, k ∈ Z;[x = ±π/3 + πk, k ∈ Z.

   Ответ: π/16 + πk/8; ±π/3 + πk, k ∈ Z.