Решите уравнение cos^4 (2x) - cos^2 (4x) = 0 - id406033920230516 от помощь155 16.05.2023 23:45

Question

Алгебра: Решите уравнение cos^4 (2x) - cos^2 (4x) = 0

помощь155 · Accepted Answer

Sinx + siny = 1/2
sinx * siny = -1/2

sinx = 1/2 - siny
(1/2 - siny)*siny = -1/2

sinx = 1/2 - siny
1/2siny - sin²y + 1/2 = 0

siny = t
1/2t - t² + 1/2 = 0
t² - 1/2t - 1/2 = 0
2t² - t - 1 = 0
t = 1
t = -1/2

siny = 1
siny = -1/2

sinx₁ = 1/2 - siny₁
siny₁ = 1

sinx₁ = -1/2
siny₁ = 1

x₁ = -π/6 + 2πn
x₂ = -5π/6 + 2πn
y₁ = π/2 + 2πn

sinx₃ = 1/2 - siny₂
siny₂ = -1/2

sinx₃ = 1
siny₂ = -1/2

x₃ = π/2 + 2πn
y₂ = -π/6 + 2πn
y₃ = -5π/6 + 2πn

ответ: (π/2 + 2πn; -π/6 + 2πn); (π/2 + 2πn; -5π/6 + 2πn); (-π/6 + 2πn; π/2 + 2πn); (-5π/6 + 2πn; π/2 + 2πn); n∈Z

Решите уравнение cos^4 (2x) - cos^2 (4x) = 0

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