Решите уравнение 1+соs x=2sin^2 x

Решите уравнение
1+соs x=2sin^2 x
- Предмет:
  Алгебра
- Автор:
  kingstonzt8y
- 5 лет назад

Ответы 1

$1 + cosx = 2sin^2x \\ \\ 1 + cosx = 2 - 2cos^2x \\\\ 2cos^2x + cosx - 1 = 0$ Пусть $t = cosx, \ |t| \leq 1$ $2t^2 + t - 1 = 0 \\ \\ D = 1 + 8 = 9 = 3^2 \\ \\ t_1 = \dfrac{-1 + 3}{4} = \dfrac{1}{2} \\ \\ t_2 = \dfrac{-1 - 3}{4} = -1$ Обратная замена: $cosx = \dfrac{1}{2} \\ \\ \boxed{x = \pm \dfrac{ \pi }{3} + 2 \pi n, \ n \in Z }\\ \\ cosx = -1 \\ \\ \boxed{x = \pi + 2 \pi n, \ n \in Z}$
- Автор:
  layne
- 5 лет назад
- 0
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Решите уравнение 1+соs x=2sin^2 x

Ответы 1

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Решите уравнение
1+соs x=2sin^2 x