6sin^2x-4sin2x=-1 Решение ...

6sin^2 (x) - 4sin (2x) = - 1 = 0;

6sin^2 (x) - 8sin (x) cosx + 1 = 0;

6sin^2 (x) - 8sin (x) cosx + sin^2 (x) + cos^2 (x) = 0;

7sin^2 (x) - 8sin (x) cosx + cos^2 (x) = 0;

Делим на cos^2 (x) ≠ 0;

7tg^2 (x) - 8tg (x) + 1 = 0;

Пусть tg (x) = y;

7y^2 - 8y + 1 = 0;

D = 36;

y1 = (8 + 6) / 14 = 1;

y2 = (8 - 6) / 14 = 2/14 = 1/7;

1) tgx = 1 = => x = п/4 + пn, n∈Z.

2) tgx = 1/7 = => x = arctg (1/7) + пk, k∈Z.

Ответ: x = п/4 + пn, n∈Z; x = arctg (1/7) + пk, k∈Z.