Решите уравнение: 1)tg^2(5x+pi/3)=3 2)sin6x×cos6x=-1/2

   1) Функция тангенс имеет период π:

• tg^2(5x + π/3) = 3;
• tg(5x + π/3) = ±√3;
• 5x + π/3 = ±π/3 + πk, k ∈ Z;
• 5x = ±π/3 - π/3 + πk, k ∈ Z;

• [5x = -π/3 - π/3 + πk, k ∈ Z;[5x = π/3 - π/3 + πk, k ∈ Z;
• [5x = -2π/3 + πk, k ∈ Z;[5x = πk, k ∈ Z;
• [5x = π/3 + πk, k ∈ Z;[5x = πk, k ∈ Z;
• [x = π/15 + πk/5, k ∈ Z;[x = πk/5, k ∈ Z.

   2) Синус двойного угла:

• sin6x * cos6x = -1/2;
• 2sin6x * cos6x = -1;
• sin12x = -1;
• 12x = -π/2 + 2πk, k ∈ Z;
• x = -π/24 + πk/6, k ∈ Z.

   Ответ:

• 1) π/15 + πk/5; πk/5, k ∈ Z;
• 2) -π/24 + πk/6, k ∈ Z.