5Sin²x - Cos²x = 4 + 4Sinx*Cosx
5Sin²x - Cos²x = 4Sin²x + 4Cos²x + 4Sinx*Cosx
5Sin²x - Cos²x - 4Sin²x - 4Cos²x - 4Sinx*Cosx = 0
Sin²x - 4Sinx*Cosx - 5Cos²x = 0 / Cos²x
tg²x - 4tgx - 5 = 0
1) Замена: tgx = t
t² - 4t - 5 = 0
t₁ = -1
t₂ = 5
2) tgx = -1
x = -π/4 + π*n, n ∈ Ζ
tgx = 5
x = arctg5 + π*n, n ∈ Ζ