Question

2 SENX-JS Cosx = 1 I​

Answer 1

Resposta:

x = π/2 + kπ , k ∈ Z  ou

x = arctg(2√5/5) + kπ, k ∈ Z

Explicação passo a passo:

senx - √5cosx = 1

Quadrando

sen²x -2√5senxcox + 5cos²x = 1²

1 - cos²x - 2√5 senx cosx + 5cos²x = 1

4cos²x - 2√5senx cosx = 0

2cosx( 2cosx - √5senx) = 0

2cosx = 0

cosx = 0 ⇒ x = π/2 + kπ , k ∈ Z

ou

2cosx - √5senx = 0

2cosx = √5 senx

senx / cosx = 2/√5

tgx = 2√5/5

x = arctg(2√5/5) + kπ, k ∈ Z