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hop1234
@hop1234
August 2022
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1)2cos(в квадрате)2x-2sin(в квадрате)2х=корень из 2
2)корень из 3 sinx-cosx=0
3)cos( в квадрате)х +cosx-7=0
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HUH39I
Verified answer
2cos²2х - 2sin²2х = √2
cos²2х - sin²2х = √2/2
cos4x = √2/2
х = ±π/16 + πn/2, n ∈ Z.
√3sinx - cosx = 0
2sin(x - π/6) = 0
x = π/6 + πn, n ∈ Z.
cos²x + cosx - 7 = 0
Пусть у = cosx <=> -1 <= y <= 1.
Область значений функции f(y) = y² + y при -1 <= у <= 1 - область [0,25; 2]. Значит -0,25 <= cos²x + cosx <= 2. Вычитаем 7, получаем -7,25 <= cos²x + cosx - 7 <= -5. Корней нет.
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Verified answer
2cos²2х - 2sin²2х = √2cos²2х - sin²2х = √2/2
cos4x = √2/2
х = ±π/16 + πn/2, n ∈ Z.
√3sinx - cosx = 0
2sin(x - π/6) = 0
x = π/6 + πn, n ∈ Z.
cos²x + cosx - 7 = 0
Пусть у = cosx <=> -1 <= y <= 1.
Область значений функции f(y) = y² + y при -1 <= у <= 1 - область [0,25; 2]. Значит -0,25 <= cos²x + cosx <= 2. Вычитаем 7, получаем -7,25 <= cos²x + cosx - 7 <= -5. Корней нет.