Sin^2x+3sinxcosx=4cos^2x

Question

Sin^2x+3sinxcosx=4cos^2x

Answer 1

Решение
Sin^2x+3sinxcosx=4cos^2x 
Sin²x + 3sinxcosx - 4cos²x = 0 делим на cos²x ≠ 0
tg²x + 3tgx - 4 = 0
tgx = t
t² + 3t - 4 = 0
t₁ = - 4
t₂ = 1
1)  tgx = - 4
x₁ = arctg(-4) + πk, k ∈ Z
x₁ = - arctg(4) + πk, k ∈ Z

2) tgx = 1
x₂ = π/4 + πn, n ∈ Z