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Шаен
@Шаен
July 2022
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a)sin^2 x+sin x+ctg^2 x+cos^2 x=0
б) Укажите все корни этого уравнения, принадлежащие промежутку [0;(7*pi)/4]
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flsh
Sin²x + sin x + ctg²x + cos²x = 0
1 + sin x + ctg²x = 0
sin x + 1/sin²x = 0
sin³x+1 / sin²x = 0
sin³x = -1
sin x ≠ 0
sin x = -1
sin x ≠ 0
x = -π/2 + 2πn, n ∈ Z
x ≠ πk, k ∈ Z
x ∈ [0; 7π/4]
x = 3π/2
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Answers & Comments
1 + sin x + ctg²x = 0
sin x + 1/sin²x = 0
sin³x+1 / sin²x = 0
sin³x = -1
sin x ≠ 0
sin x = -1
sin x ≠ 0
x = -π/2 + 2πn, n ∈ Z
x ≠ πk, k ∈ Z
x ∈ [0; 7π/4]
x = 3π/2