Cos^2x-Sin^2x=Cosx-Sinx
Cos^2x-Sin^2x -( Cosx-Sinx) = 0
(Cosx - Sinx)(Cosx + Sinx) - (Cosx -Sinx) = 0
(Cosx -Sinx)(Cosx +Sinx -1) = 0
Cosx - Sinx = 0|:Cosx или Cosx +Sinx -1 = 0
1 - tgx = 0 (1 - tg²x/2) /(1 + tg²x/2) + 2tgx/2/(1 + tg²x/2) = 1
x = π/4 + πk , k ∈Z 1 - tg²x/2 + 2tx/2 = 1 + tg²x/2
2tg²x/2 -2tgx/2 -1 = 0
tgx/2 = (1 +-√3)/2
x/2 = arctg((1 +-√3)/2) + πn, n∈Z
x = 2 arctg((1 +-√3)/2) + πn, n∈Z