Question

sin2x + 5 sin x cos x + 2 cos2x = -1

Answer 1

Ответ:

Объяснение:

РешениеSin²x + 5sinxcosx + 2cos²x = - 1 Sin²x + 5sinxcosx + 2cos²x = - sin²x - cos²x

2sin²x + 5sinxcosx + 3cos²x = 0 делим на cos²x ≠ 02tg²x + 5tgx + 3 = 0

tgx = t

2t² + 5t + 3 = 0

D = 25 - 4*2*3 = 1

t₁ = (- 5 - 1)/4 = - 6/4 = - 3/2 = - 1,5

t₂ = (- 5 + 1)/4 = - 1

1)  tgx = - 3/2

x₁ = - arctg(1,5) + πk, k ∈ Z

2)  tgx = - 1

x₂ = - π/4 + πn, n ∈ Z