1) sin 2x = 0,5 2) cos 2x = 0,5 3) - 3tgx=3 4) 2ctgx=2

Найдем корни уравнений.

1) sin (2 * x) = 0,5;

sin (2 * x) = 1/2;

2 * x = (-1) ^n * arcsin (1/2) + пи * n, n ∈ Z;

2 * x = (-1) ^n * пи/6 + пи * n, n ∈ Z;

x = (-1) ^n * пи/12 + пи/2 * n, n ∈ Z;

2) cos (2 * x) = 0,5;

cos (2 * x) = 1/2;

2 * x = + -arccos (1/2) + 2 * пи * n, n ∈ Z;

2 * x = + -пи/3 + 2 * пи * n, n ∈ Z;

x = + -пи/6 + пи * n, n ∈ Z.

3) - 3 * tg x = 3;

tg x = - 3/3;

tg x = - 1;

x = arctg (-1) + пи * n, n ∈ Z;

x = 3 * пи/4 + пи * n, n ∈ Z;

4) 2 * ctg x = 2;

ctg x = 2/2;

ctg x = 1;

x = arcctg (1) + пи * n, n ∈ Z;

x = пи/4 + пи * n, n ∈ Z.