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toseshevaanna
@toseshevaanna
August 2022
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Решить:
1-sin x/2=cos х
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nKrynka
Решение
1-sin x/2=cos х
1 - sin x/2 = 1 - 2sin
²(x/2)
2sin
²(x/2) - sin(x/2) = 0
sin(x/2) * (2sin(x/2) - 1) = 0
1) sin(x/2) = 0
x/2 = πk, k ∈Z
x₁ = 2πk, k ∈ Z
2)
2sin(x/2) - 1 = 0
2sin(x/2) = 1
sin(x/2) = 1/2
x/2 = (-1)^n * arcsin(1/2) + πn, n ∈Z
x/2 = (-1)^n * (π/6)
+ πn, n ∈Z
x₂ = (-1)^n * (π/3)
+ 2πn, n ∈Z
Ответ: x₁ = 2πk, k ∈ Z ; x₂ = (-1)^n * (π/3)
+ 2πn, n ∈Z
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Answers & Comments
1-sin x/2=cos х
1 - sin x/2 = 1 - 2sin²(x/2)
2sin²(x/2) - sin(x/2) = 0
sin(x/2) * (2sin(x/2) - 1) = 0
1) sin(x/2) = 0
x/2 = πk, k ∈Z
x₁ = 2πk, k ∈ Z
2) 2sin(x/2) - 1 = 0
2sin(x/2) = 1
sin(x/2) = 1/2
x/2 = (-1)^n * arcsin(1/2) + πn, n ∈Z
x/2 = (-1)^n * (π/6) + πn, n ∈Z
x₂ = (-1)^n * (π/3) + 2πn, n ∈Z
Ответ: x₁ = 2πk, k ∈ Z ; x₂ = (-1)^n * (π/3) + 2πn, n ∈Z