5sin2x-cos2x=4+4sinx*cosx

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