5sin^2x-cos^2x=4+4sinxcosx

5Sin²x - Cos²x = 4 + 4Sinx*Cosx 5Sin²x - Cos²x = 4*(Sin²x + Cos²x) + 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

Решение. 5*(sin(x))^2-(cos(x))^2=4+4*sin(x)*cos(x);(sin(x))^2-5*(cos())^2-4*sin(x)*cos(x)=0; (tg(x))^2-4*tg(x)-5=0; tg(x)1=5; tg(x)2=-1; Дальше самостоятельно.