решите уравнение 2sin(x-p/2)*cos(p/2+x) +корень из трех cosx Cosx не под корнем. Created by аня7399. algebra-ru

2+x) +корень из трех cosx Cosx не под корнем...

аня7399 @аня7399

June 2022 1 12 Report

решите уравнение
2sin(x-p/2)*cos(p/2+x) +корень из трех cosx
Cosx не под корнем

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nKrynka

Verified answer

Решение
- 2сosx*(- sinx) + √3cosx = 0
2sinx*cosx + √3cosx = 0
cosx(2sinx + √3) = 0
1) cosx = 0
x₁ = π/2 + πk, k ∈ Z
2) 2sinx + √3 = 0
sinx = - √3/2
x = (-1)^(n+1)arcsin(√3/2) + πn, n ∈ z
x₂ = (-1)^(n+1)*(π/3) + πn, n ∈ Z

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