2sin²x - sinxcosx = cos²x
2sin²x - sinxcosx - cos²x = 0
Разделим на cos²x.
2tg²x - tgx - 1 = 0
Пусть t = tgx.
D = 1 + 8 = 9 = 3²
t1 = (1 + 3)/4 = 1
t2 = (1 - 3)/4 = -1/2.
Обратная замена:
tgx = 1
x = π/4 + πn, n ∈ Z
tgx = -1/2
x = arctg(-1/2) + πn, n ∈ Z.