cos2x=√√2(cos x-sin x)
cos2x - √2(cos x-sin x) = 0
Сos²x - Sin²x - √2(cos x-sin x)= 0
(Cosx - Sin x)(Cosx + Sin x) - √2(cos x-sin x) = 0
(Cos x - Sin x)(Cos x + Sinx -√2) = 0
Cos x - Sin x = 0 | : Сos x ≠0 или Сos x + Sin x - √2 = 0
1 - tg x = 0 (1-tg²x/2)/(1 + tg²x/2)+2tgx/2/(1 + tg²x/2)= √2
tgx = 1 tgx/2 = 0 или tgx/2 = 1
x = π/4 + πk , k ∈Z x/2 = πn, n ∈Z x/2 = π/4 + πm, m ∈Z
х = 2πn, n ∈Z x = π/2 + 2πm, m∈Z