3sin²x + 2sin x cos x - cos²x = 2
3sin²x + 2sin x cos x - cos²x = 2sin²x + 2cos²x
sin²x + 2sin x cos x - 3cos²x = 0 | ÷ cos²x; cos x ≠ 0
tg²x + 2tg x - 3 = 0
tg x = t
t² + 2t - 3 = 0
D = 4 + 12 = 16 = 4²
t = (-2 ± 4) ÷ 2
t₁ = -3; t₂ = 1
tg x = -3; x = arctg(-3) + πk, k ∈ Z
или
tg x = 1; x = π/4 + πn, n ∈ Z
3sin²x + 2sin x cos x - cos²x = 2
3sin²x + 2sin x cos x - cos²x = 2sin²x + 2cos²x
sin²x + 2sin x cos x - 3cos²x = 0 | ÷ cos²x; cos x ≠ 0
tg²x + 2tg x - 3 = 0
tg x = t
t² + 2t - 3 = 0
D = 4 + 12 = 16 = 4²
t = (-2 ± 4) ÷ 2
t₁ = -3; t₂ = 1
tg x = -3; x = arctg(-3) + πk, k ∈ Z
или
tg x = 1; x = π/4 + πn, n ∈ Z