Question

5sin2x-cos2x=4+4sinx*cosx

Answer 1

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