Sin(2x) + cos(2x) = 0
2sinx*cosx + cos^2(x) - sin^2(x) = 0 - разделим обе части уравнения на (-cos^2(x))
tg^2(x) - 2tg(x) - 1 = 0
Замена: tgx = t
t^2 - 2t - 1 = 0
D = 4 + 4 = 8
t1 = (2 - 2√2)/2 = 1 - √2
t2 = 1 + √2
1) tgx = 1 - √2
x = arctg(1-√2) + πk, k∈Z
2) tgx = 1+√2
x = arctg(1+√2) + πk, k∈Z