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Aleksandra56
@Aleksandra56
November 2021
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Помогите,пожалуйста. Решить-решила,но хочется знать,так или нет)
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nKrynka
Решение
1/2*sin2x + sin∧2x - sinx = cosx
1/2*2sinxcosx + sin∧2x - sinx - cosx = 0
sinx(cosx + sinx) - (cosx + s-nx) = 0
(cosnx + sinx)*(sinx - 1) = 0
1) cosnx + sinx = 0 / cosnx ≠
1 + tgx = 0
tgx = -1
x = - π/4 ∈ [-2π;-π/2]
2) sinx - 1 = 0
sinx = 1
x = π/2 ∉ [-2π;-π/2]
Ответ: x = - π/4 ∈ [-2π;-π/2]
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Answers & Comments
1/2*sin2x + sin∧2x - sinx = cosx
1/2*2sinxcosx + sin∧2x - sinx - cosx = 0
sinx(cosx + sinx) - (cosx + s-nx) = 0
(cosnx + sinx)*(sinx - 1) = 0
1) cosnx + sinx = 0 / cosnx ≠
1 + tgx = 0
tgx = -1
x = - π/4 ∈ [-2π;-π/2]
2) sinx - 1 = 0
sinx = 1
x = π/2 ∉ [-2π;-π/2]
Ответ: x = - π/4 ∈ [-2π;-π/2]