Помогите, пожалуйста, решить данный пример [tex]sinx \geq cos2x[/tex]. Created by namotrasnik. algebra-ru

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namotrasnik @namotrasnik

July 2022 1 3 Report

Помогите, пожалуйста, решить данный пример
[tex]sinx \geq cos2x[/tex]

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sedinalana

Verified answer

Sinx-1+2sin²x≥0
sinx=a
2a²+a-1≥0
D=1+8=9
a1=(-1-3)/4=-1 U a2=(-1+3)/4=1/2
a≤-1⇒sinx≤-1⇒sinx=-1⇒x=-π/2+2πn
a≥1/2⇒sinx≥1/2⇒x∈[π/6+2πn;5π/6+2πn]
Ответ x∈[π/6+2πn;5π/6+2πn] U {-π/2+2πn},n∈z

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namotrasnik August 2022 | 0 Ответы

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namotrasnik August 2022 | 0 Ответы

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