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Алекссеевна
@Алекссеевна
July 2022
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Помогите пожалуйста!)
sin x + sin 3x=4cos^2x
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Answers & Comments
nKrynka
sin x + sin 3x = 4cos
²
x
2sin(x + 3x)/2*cos(x - 3x)/2 = 4cos
²x
2sin2x*cosx - 4cos²x = 0
4sinxcos²x - 4cos²x = 0
4cos²x(sinx - 1) = 0
1) cos²x = 0
x₁ = π/2 + πn, n∈Z
2) sinx - 1 = 0
sinx = 1
x₂ = π/2 + 2πk, k∈Z
2 votes
Thanks 4
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Answers & Comments
2sin(x + 3x)/2*cos(x - 3x)/2 = 4cos²x
2sin2x*cosx - 4cos²x = 0
4sinxcos²x - 4cos²x = 0
4cos²x(sinx - 1) = 0
1) cos²x = 0
x₁ = π/2 + πn, n∈Z
2) sinx - 1 = 0
sinx = 1
x₂ = π/2 + 2πk, k∈Z