cos2x + sinx*cosx + cos²x = 1
2cos²x - 1 + sinx*cosx + cos²x - 1 = 0
3 cos²x + sinx*cosx - 2 = 0
3 cos²x + sinx*cosx - 2sin²x-2cos²x = 0
cos²x + sinx*cosx - 2sin²x = 0 | : cos²x ≠ 0
1 + tgx - 2tg²x = 0
2tg²x - tgx - 1 = 0
Пусть tgx = t, t ∈ R
2t² - t - 1 = 0
D = 1 +4*2 = 9, √D = 3
t1 = 1 + 3 /4 = 1
t2 = 1 - 3 /4 = - 1/2
tg x = 1 или tgx = -1/2
x = π/4 + πk, k∈Z и x = -arctg 1/2 + πk, k∈ Z