Помогите с тригонометрией! Уравнение в приложении. Created by mrnobodyyyy. algebra-ru

Помогите с тригонометрией! Уравнение в приложении...

March 2022 1 11 Report

Помогите с тригонометрией! Уравнение в приложении

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nKrynka Решение
4 - cos²3x = 3sin²3x + 2sin6x
4 - cos²3x - 3sin²3x - 2sin6x = 0
4 - 3*(cos²3x + sin²3x) - 2sin6x = 0
4 - 3 - 2sin6x = 0
1 - 2sin²6x = 0
sin²6x = 1/2
1) sin6x = - √2/2
6x = (-1)^n * arcsin(- √2/2) + πk, k ∈ Z
6x = (-1)^(n+1) * arcsin(√2/2) + πk, k ∈ Z
6x = (-1)^(n+1) * arcsin(√2/2) + πk, k ∈ Z
6x = (-1)^(n+1) * (π/4) + πk, k ∈ Z
x₁ = (-1)^(n+1) * (π/24) + πk/6, k ∈ Z
2) sin6x = √2/2
6x = (-1)^n * (π/4) + πn, n ∈ Z
x₂ = (-1)^n * (π/24) + πn/6, n ∈ Z

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