2 sin ² x - sin x cos x - cos² x = 0

2 sin ^2 x - sin x cos x - cos^2 x = 0; / /делим каждый член на cos^2x

2 sin^2x/cos^2x - sinxcosx/cos^2x - cos^2x/cos^2x = 0/cos^2x;

2tg^2x - tgx - 1 = 0;

Пусть tgx = a = > tg^2x = a^2;

2a^2 - a - 1 = 0;

D = (-1) ^2 - 4 * 2 * (-1) = 1 + 8 = 9;

a = (1 + - 3) / 4;

a1 = 1;

a2 = - 1/2;

tgx = 1, tgx = - 1/2;

x = п/4 + пk, k ∈ Z;

x = arctg (-1/2) + pik, k ∈ Z.

Ответ:

п/4 + пk, k ∈ Z;

arctg (-1/2) + pik, k ∈ Z.