1) 2sinx + sin2x=0 2) tgx-3ctgx=0

Найдем корешки.

1) 2 * sinx + sin (2 * x) = 0;

2 * sin x + 2 * sin x * cos x = 0;

2 * sin x * (1 + cos x) = 0;

sin x = 0;

1 + cos x = 0;

sin x = 0;

cos x = -1;

x = п * n, n Z;

x = -п + 2 * п * n, n Z;

Ответ: x = п * n, n Z и x = -п + 2 * п * n, n Z.

2) tg  x 3 * ctg x = 0;

tg x 3 * 1/tg x = 0;

tg x * tg x 3 * 1/tg x * tg x = 0;

tg^2 x 3 = 0;

(tg x - 3) * (tg x + 3) = 0;

tg x - 3 = 0;

tg x + 3 = 0;

tg x = 3;

tg x = -3;

x = atc tg (3) + pi * n, n Z;

x = arctg (-3) + pi * n, n Z;

x = pi/3 + pi * n, n Z;

x = -pi/3 + pi * n, n Z.