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.