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ELOGE
@ELOGE
August 2022
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Решить уравнение cos (3x +П/6)+ cos (x + П/4 ) = 0
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sharadi
Сos (3x +π/6)+ Сos (x + π
/4 ) = 0
есть формула: Cos
α + Cosβ = 2Sin(α+β)/2 * Sin(α-β)/2
применим её:
2Sin(3x +π/6 +x +π/4)/2 * Sin((3x +π/6 -x -π/4)/2= 0
2Sin(2x +5π/24) *Sin(x -π/24) = 0
Sin(2x +5π/24) = 0 или Sin(x -π/24)= 0
2х + 5π/24 = πn, n ∈Z x - π/24 = πm, m ∈Z
2x = πn - 5π/24, n ∈ Z
x = πm + π/24 , m ∈Z
x = πn/2 -5π/48, n ∈Z
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Answers & Comments
есть формула: Cosα + Cosβ = 2Sin(α+β)/2 * Sin(α-β)/2
применим её:
2Sin(3x +π/6 +x +π/4)/2 * Sin((3x +π/6 -x -π/4)/2= 0
2Sin(2x +5π/24) *Sin(x -π/24) = 0
Sin(2x +5π/24) = 0 или Sin(x -π/24)= 0
2х + 5π/24 = πn, n ∈Z x - π/24 = πm, m ∈Z
2x = πn - 5π/24, n ∈ Z x = πm + π/24 , m ∈Z
x = πn/2 -5π/48, n ∈Z