6sin^2x-4sin2x=-1Решение..

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.