Question

Решите уравнение 3sin2(x)+2sin(x)cos(x)−cos2(x)=23sin2(x)+2sin(x)cos(x)−cos2(x)=2.

Answer 1

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