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NormanRed
@NormanRed
June 2022
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4 tg^2x+tgx-3=0
Розвязать тригонометрические уравнение , срочно
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nKrynka
Решение
4 tg^2x+tgx-3=0
tgx = t
4t² + t - 3 = 0
D = 1 + 4*4*3 = 49
t₁ = (- 1 - 7)/8
t₁ = - 1
t₂ = (- 1 + 7)/8
t₂ = 3/4
1) tgx = - 1
x₁ = - π/4 + πk, k∈Z
2) tgx = 3/4
x₂ = arctg(3/4) + πn, n ∈Z
Ответ: x₁ = - π/4 + πk, k∈Z ; x₂ = arctg(3/4) + πn, n ∈Z
6 votes
Thanks 9
NormanRed
Благодарю за помощь , это сильно мне поможет
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Answers & Comments
4 tg^2x+tgx-3=0
tgx = t
4t² + t - 3 = 0
D = 1 + 4*4*3 = 49
t₁ = (- 1 - 7)/8
t₁ = - 1
t₂ = (- 1 + 7)/8
t₂ = 3/4
1) tgx = - 1
x₁ = - π/4 + πk, k∈Z
2) tgx = 3/4
x₂ = arctg(3/4) + πn, n ∈Z
Ответ: x₁ = - π/4 + πk, k∈Z ; x₂ = arctg(3/4) + πn, n ∈Z